Corrections to
We extend our thanks to the many readers who have reported errors in our
book. We hope that the corrections will
bring our book closer to that level of technical perfection that students
long for but authors find so elusive.
Errors that were reported before March 2001 are corrected in the
summer 2001 printing and in more recent printings of our textbook.
These errors are corrected in any printing of the book with 'Westview'
or 'CRC Press'
on the spine. The same corrections are made in the Chinese and Indian
paperback editions. If you own such a book, please skip directly to the
list of errors reported since March 2001.
Our book has recently gone through several changes of publishers and
printings. The book was originally published by Addison-Wesley in
1995, in their Frontiers in Physics series. Our current publisher is Taylor and Francis (CRC
Press). The Taylor and Francis edition is
identical inside the covers to the older Westview press edition.
This edition also has the same
errors as the Westview edition, though we are promised a new printing
with further error corrections in the future. If you try to find
this book on the Taylor and Francis site, you may find a page that
says our book is out of print. That is not correct. Please click the link
for "CRC Press" above, or go to Amazon.com.
If you buy our book from Amazon, DO NOT buy the Kindle edition. It is
not possible to read the subscripts of subscripts on a Kindle, and
there are many examples of these in the book.
Over the years, many people have asked for written solutions to the
problems in the book. Recently, Zhong-Zhi Xianyu put considerable
effort into writing up a complete set of solutions in very clear
format. Xianyu's solutions are now available to you at
this link. I hope that these solutions are useful to those of
you who have struggled too hard already with the problems in this
book---but also that their availability
will not be too tempting for those who have
not struggled hard enough. We endorse these solutions, but they are
not free of errors. If you find errors in the solutions, please send
email
and we will post the errors at the bottom of the book errata below.
When Michael Peskin taught the Quantum Field Theory course at
Stanford in the mid 2000's, he added some material that is not included in the textbook.
We provide the new lectures here in the hope that they might
be useful:
In addition, Michael Peskin has put on the arXiv some additional pedagogical
lecture notes. A set of notes on calculational methods for QCD at
colliders, supplementing the discussion of Chapter 17,
can be found at:
A set of notes on the theory of the weak interactions and the Higgs
boson, including an improved discussion of the Goldstone Boson
Equivalence Theorem, can be found at:
We hope that readers of our book will find these lecture notes useful.
The book states in several places that it is not a textbook of
elementary particle physics. Recently, Michael Peskin has published a
textbook of elementary particle physics that covers the important
phenomena of this subject and presents the data that supports the
current Standard Model of Particle Physics:
"Concepts of Elementary
Particle Physics" (Oxford University Press, 2019). That book does
not assume a knowledge of Quantum Field Theory but does cover some of
the topics in this book at a lower theoretical level. I hope that
"theoretical theory"-oriented students will look at that book to
understand better how Quantum Field Theory applies to real-world physics.
Roni Harnik recently presented to us
some
evidence that our book is in good taste.
Marilena Loverde and Laura Newburgh provided us with a photo-essay
on the ATLAS experiment (created for the 2012 Washington Post Peeps
competition) that demonstrates that our textbook is
essential equipment at the LHC: overview
of ATLAS; essential
textbooks.
Errors that were reported before August 1997 are corrected in the
fifth printing (December 1997) and in more recent printings of our textbook.
Those errors are corrected in any printing of the book with `Perseus'
on the spine. If you own such a book, however, you might wish to look at
the
list
of errors reported from 1997 to 2001. Two lengthy notes (to p. 46 and
p. 79) were not included in the more recent corrected printings,
and these are transferred to the list on this page.
The list of errors in the original edition of our book is quite long.
Only a few of these errors have important consequences. However, there
are many minor errors in individual derivations. We have therefore
reorganized the list into a catalogue of
Owners of the first four printings might wish to mark only the errors in
the highest category and keep the rest of the list for reference.
For those who would like a complete list of the errors, we have also
prepared catalogues of
We would be most grateful to hear of any further errors that are not listed
on these pages. Please send them by e-mail to
mpeskin@slac.stanford.edu.
Errors reported since March 2001, updated April 2022:
Notations and Conventions:
Chapter 2:
- p. 18: [The following correction has been here for some time, but
it was posted in error and should be removed. We apologize. Eq. (2.15)
is consistent given the definition of Delta in (2.9). The incorrect
correction read: In eq. (2.15), the factor of "alpha" on the left-hand
side of each equation should be omitted. (Thanks to R. Kallosh
for straighting us out.)]
- p. 28: Two lines under eq. (2.53), the phrase "since each term is
separately Lorentz invariant" should properly read "since each term is
separately invariant under continuous Lorentz transformations". (Thanks
to T. Wettig.)
Chapter 3:
- p. 36: In line 5 below eq. (3.1), "by a boost" should read
"by a rotation or a boost". (Thanks to L. Fillion.)
- p. 42: In the unnumbered equation at the bottom of the page, please
note that the notation "del_nu psi(Lambda^{-1}x)" means
"del/del y^nu psi(y), evaluated at y = Lambda^{-1}x". Thus,
del/del x^mu psi(Lambda^{-1}x)
= (Lambda^{-1})^nu_mu del_nu psi(Lambda^{-1}x).
This is the origin of the factor (Lambda^{-1})^nu_mu on the
right-hand side of the first line.
(Thanks to J. Fredsted).
- p. 46: On this page, the spinors u(p) are represented using
square roots of matrices: sqrt(p.sigma) and sqrt(p.sigmabar).
It is useful to note that these objects can be rewritten
without square roots of matrices
as: sqrt(p.sigma) = (p.sigma + m)/sqrt(2(p^0 + m)) , and similarly
for sigmabar, for a 4-vector p such that p^2 = m^2.
(Thanks to Prof. A. Sirlin!)
- p. 46: Just above eq. (3.49), "Now apply the same boost to u(p)"
should read "Now apply the same boost to u(p_0)". (Thanks to L. Fillion.)
- p. 51: Several people have asked about the minus signs in the
discussion of Fierz identities. They are correct. However, these
formulae assume c-number u(p) spinors and sigma matrices. Typically,
these formulae are applied in working with operators containing spinor
fields. In that case, there is an extra minus sign from spinor
anticommutation. See, e.g., p. 608, below eq. (18.43). (Thanks to
Sacha Davidson.)
- p. 53: Notice that eq. (3.89) is a matrix equation. For
more clarity, on the left-hand side, one might put the index a on
psi(x) and b on psi^dagger(y). Then each line on the right-hand
side is a matrix with indices ab. (Thanks to L. Fillion.)
- p. 56: The expectation values on this page are not
Lorentz-invariant; however, they are covariant under Lorentz
transformations with the simple transformation law <...> -> S <...>
S^{-1}. So the text above eq. (3.94) should begin: "This
expression is properly covariant under boosts only if ..." (Thanks
to B. Dirgantara.)
- p. 61: In the eighth line on the page "annihiliation" should read
"annihilation". (Thanks to N. Yamanaka.)
- p. 61: In the second line below the first displayed equation, the
indices r on a^dagger operators should be changed to r'. In the
second displayed equation, u^dagger and xi^dagger should have the
index r and u and xi should have the index s. The final
result of the calculation is unchanged. (Thanks to
R. Lebed.)
- p. 64: The nomenclature in the diagram in the middle of the
page is at the very least nonstandard and even, according to sources
such as Weinberg, vol. 1, incorrect. Typically, a "proper" Lorentz
transformation is one satisfying det Lambda = 1. Then, if the
"proper orthochronous Lorentz group" is called L, TL is "improper
nonorthochronous" and PTL is "proper nonorthochronous". These names
are technically correct but give the wrong impression. A better
terminology is to use "orthochorous" for Lorentz transformations that
do not require a space inversion. Then, in the diagram "proper" and
"improper" should be replaced by "orthochorous" and
"nonorthochorous". With this terminology PTL is "nonorthochorous
nonorthochronos", which is awkward but indicates the mathematical
situation accurately. (Thanks to K. Nii.)
- p. 69: In the definition of T using flipped spins, it is
tricky to maintain consistency. Since xi^{- (-s)} = - xi^{s}, two
applications of T to a spinor give a minus sign. So it is not
exactly true that T^2 = 1, as implied in the text. Instead, T^2 =
R(2pi), a 2 pi rotation. On the space of bosonic states, or in the
transformation of bosonic operators such as fermion bilinears, T^2 = 1.
This is close enough to the identity to use T for discussions of
invariance. (Thanks to A. Agrawal.)
Chapter 4:
- p. 79: We are informed that the gauge condition "del_mu A^mu = 0", which
in every modern textbook is called the `Lorentz condition', should
actually be the `Lorenz condition'. Ludwig Valentin Lorenz,
the inventor of the retarded potential, actually wrote down this
condition in 1867, when Hendrik Antoon Lorentz was 14 years old.
It is another example of the Matthew effect at work. See
E. T. Whittaker, A History of the Theories of Aether and
Electricity, vol. 1, p. 269 and J. Van Bladel, IEEE Antennas
and Propagation Magazine, vol. 33, p. 69 (1991). (Thanks to
J. Bielawski.)
- p. 82: The derivation of eq. (4.31) in Section 4.2 assumes
that the Hamiltonian of the theory is time-independent. But,
actually, it is also important to use this equation in theories with
time-dependent Hamiltonians. The Hamiltonian may be time-dependent
when the quantum field is coupled to a fixed classical background
field, a situation considered in Section 6.2. Some derivations of
(4.31) and also the LSZ reduction formula (7.45) that you will find
in other books make use of an interaction term that is zero at time
infinity and is adiabatically turned on at a finite (negative) time
and turned off at a finite (positive) time. Thus it is important to know that the
formula (4.31) also holds for a time-dependent Hamiltonian, as long
as H_0 is time-independent. To derive the equation in this context,
replace e^{-iH(t-t0)} everywhere by u(t,t0), defined as the solution to the
equation i d/dt u(t,t0) = H(t) u(t,t0) with initial condition
u(t0,t0) = 1. The interaction
Hamiltonian will still be defined by eq. (4.19), except that now
H_int(t) is time-dependent. You can check that the entire
derivation given in Section 4.2 goes through in this more general
context. (Thanks to R. Nepomechie.)
- p. 87: In the unnumbered equation just below eq. (4.30), the
expression on the right-hand side should be preceded by the same
"lim_T -> infty(1-i epsilon)" as appears in the other equations on
this page. (Thanks to N. Sueishi.)
- p. 124: In the setence just below the figure, "Q_d" should read "Q".
(Thanks to K. Matawari.)
- p. 125: In the line below the unnumbered equation below (4.133),
the end of the line should read "vanish if {\bf p } = {\bf p'} =
0", that is, in the non-relativistic limit where the 3-momenta vanish. (Thanks to P. Bourdet.)
Chapter 5:
- p. 146: In the second line of eq. (5.32), the result should be
+ e^2( 1 - cos theta). The change of sign has no effect on the
cross section formulae. (Thanks to S. Gryba.).
- p. 147: In the 4th line from the bottom of the page, "s-wave"
should read "S-wave". (Thanks to G. Wilson.)
- p. 150: Some minus signs are missing here. Eq. (5.47) is
correct. Eqs. (5.48) and (5.49) should have a "-" on the right-hand
side in front of the "1/sqrt(2)". In the first line below
eq. (5.48), the second sentence should read "Choosing n =
-(x+iy)/sqrt(2) ..." Eqs. (5.50) and (5.51) should then also get an
extra "-" on the right hand side. None of these minus signs affect the later
results of this section. (Thanks to P. Axolotl.)
- p. 151: In eq. (5.53), please note that the denominator in the
prefactor on the right-hand side, written "2 2m 2m", is equal to
"2 2E 2E", where E in the energy of the incoming electron or
positron, since the CM energy in this process is M = 2m to a good
approximation.
(Thanks to G. Barone.)
- p. 156: There is some confusion in the paragraph just below
eq. (5.70). In the crossing procedure described, the initial electron
momentum p and the final muon momentum k remain unchanged, while the
initial positron momentum p' is continued to the momentum of a final-state
electron and the final anti-muon momentum k' is continued to the momentum
of an initial state muon. Since p and k are unchanged, (p-k)^2 is
unchanged. We wrote in the text that u is unchanged, but this is not quite
right. In e-e+ -> mu-mu+, we would naturally call (p-k)^2 = t, but in
e-mu- -> e-mu-, we would naturally call (p-k)^2 = u. So, the rearrangement
described in the text as s <-> t with u unchanged is described better
as s->t t->u u->s. However eq. (5.71) is symmetric under interchange
of s and u, so either crossing process gives the right answer. (Thanks
to C. Schubert.)
- p. 166: In the unnumbered equation just below Fig. (5.6),
the minus sign on the left-hand side of the equation should be
removed and replaced by a minus sign on the right-hand side of the
equation. Then the right-hand side of eq. (5.101)
should also be multiplied by (-1). After the matrix element is
squared, this minus sign disappears in the rest of the section.
(Thanks to P. Axolotl.)
- p. 169: In the equation in Problem 5.1, the right-hand side should
be multiplied by Z^2 to be consistent with Problem 4.4, part (c). (Thanks
to B. Souto.)
- p. 171: In the fourth line of Problem 5.3, part (d), "v_R" should be
replaced by "u_R". (Thanks to K. Matawari.)
- p. 172: In Problem 5.4, part (c), there are two issues.
First, in the formula for
|B(k)> we should have been more explicit and written: the creation
and annihilation operators as tw-component objects: a_k
= (a_1, a_2), b_k = (b_2, b_1). More importantly, the last
lines of part (c) should read: "for which a typical value
might be h^{12} = h^{21} = 1/sqrt{2} and all other components
zero." (Thanks to J. Wang.)
Chapter 6:
p. 188: At the bottom of the page, we say, "the g-factor of the
proton differs by 40% from the Dirac value." Actually, the g-factor
of the proton is 5.58, almost a factor of 3 away from Dirac. Nevertheless,
eq. (6.33) still applies, as it does for any spin-1/2 particle. The
large value of g is easily understood when the proton is modeled as a
bound state of three quarks, each of which has a g-factor close to 2.
(Thanks to R. Gerasimov.)
- p. 201: In the un-numbered equation just below Eq. (6.69),
the denominator on the right-hand side should read
"p^0 - |\vec p| cos theta". (Thanks to A. Gupta.)
- p. 208: The explanation in the full paragraph on this page is
confused. Because the contributions from different energies
factorize, eq. (6.86) is correct if we consider only the effect of
photons emitted in the energy region E- < E < E+. However, note
that the factor exp[- (alpha/pi) f_IR(q^2) log(E+^2/E-^2)] is
already included in the exponential factor in eq. (6.84). So, the
correct result is the following: The probability for electron
scattering into a solid angle dOmega emitting 0 photons with E+ < E,
n photons with E- < E < E+, 0 photons with El < E < E-, and ANY
NUMBER of (unobservable) photons with E < El is given by eq. (6.84)
multiplied by [ lambda^n/n! ], where lambda is given by eq. (6.86).
(Thanks to A. Kazantsev.)
- p. 208: In the figure associated with Problem 6.1, the right-hand
side should include a factor "ie". (Thanks to K. Matawari.)
Chapter 7:
- p. 215, 7 lines below eq. (7.10), the equation for the field
strength renormalization factor Z should read "Z = < Omega | phi(0)
| mu_0> |^2", where {|mu_p>} are the exact 1-particle states. You
might want to write this equation simply as "Z = < Omega | phi(0)
|p = 0> |^2", using the states {|p>} in eq. (7.1). We use the
symbol mu to emphasize that the states contributing to Z are exact
eigenstates of the Hamiltonian rather than free-field states or
other approximate 1-particle states. (Thanks to A. Agrawal.)
- p. 218: Directly below eq. (7.20), "Sigma_2(p^2)" should read
"Sigma_2(p)". However, the comment refers to the analytic functions
that multiply "m_0" and "pslash" in eq. (7.19), considered as functions
of the complex variable "p^2". (Thanks to L. Gerland.)
- p. 222: In the footnote, the reference should read: Nuovo Cimento
1, 205 (1955). (Thanks to R. Vaidya.)
- p. 224: In first line of eq. (7.40), which appears at the bottom
of this page, there should be an additional factor
exp[ i (p_0 - E_k + i epsilon)T_+ ]. However, this factor
should not appear in the second line of eq. (7.40), at the top
of p. 225, which includes the pole term only. (Thanks to K. Arai.)
- p. 225: In the second line of eq. (7.40), at the top of this page,
the expression under the tilde should read "p^0 -> + E_k".
(Thanks to Y. Wu.)
- p. 236: There is an important omission in the statement of the
Cutkosky rules. After step 2, there should be
another step: 3. On the far side of the cut, replace +i epsilon in
all uncut propagators by -i epsilon. Then, 4. Sum the
contributions of all possible cuts. The added step is irrelevant
for 1-loop diagrams, but for higher-loop diagrams it accomplishes
the complex conjugation needed to obtain the optical theorem at
these orders. (Thanks to J. Donoghue.)
- p. 243: In the equation just below the figure at the top of the page,
"m" in the denominator should be replaced by the bare mass "m_0".
Actually, all of the formulae in this section use "m" to
represent the bare mass of the electron, but now it becomes
very important to recognize this explicitly. That is because,
in the argument on this page, we use the result of Section 7.1
to rewrite the singularity in the exact propagator in the
form of the second equation above (7.70), where now "m"
is the physical mass of the electron. If you are careful
about these distinctions, you will see that the final conclusion
of the section, eq. (7.70), is correct. (Thanks to S. Pi.)
Chapter 8:
Chapter 9:
- p. 279: Just above the unnumbered equation at the bottom of the page,
"(9.4)" should read "(9.5)". (Thanks to J. Larsen.)
- p. 305: The trace in the first line of the right-hand side of eq. (9.80) should read:
"tr[(-ie Aslash(x1)) S_F(x1-x2) (-ie Aslash(x2)) S_F(x2-x3) ... (-ieAslash(xn)) S_F(xn-x1) ] ".
(Thanks to M. Smedback.)
- p. 312: In Problem 9.1, part (c), "Pi^{mu nu}(q^2)" should read
"Pi^{mu nu}(q)". (Thanks to K. Matawari.)
Chapter 10:
- p. 336: In the first line of eq. (10.50), the first factor alpha
should be omitted, since it is already included in Pi_2(q^2).
(Thanks to W. Kaufmann.)
- p. 337: On the last line in the page, "Bogoliubov" should be
"Bogolubov". In "Introduction to Axiomatic Field Theory", by
Bogolubov, Logunov, and Todorov, the translator notes that
Bogolubov requested that his name be transliterated in this way.
The same change is needed in the Index, p. 819.
(Thanks to L. Fillion.)
- p. 345: In Problem 10.4, the numerical coefficient in the order
lambda^3 term should be "3/2", not "5/2". (I am very grateful to
D. Lee for bring this to my attention, and I apologize to any reader
who has suffered greatly over this problem only to reach an answer
different from that in the text.)
Chapter 11:
- p. 355: In the third equation in (11.17), the left-hand side
should read: " i Im ( .. ) = ". (Thanks to C. Locke.)
- p. 362: In the second unnumbered equation, the numerator of
the propagator should be i, not 1. (Thanks to C. Zhang.)
- p. 363: The expressions in eq. (11.39) and in the unnumbered
equation just above it should be multiplied by (-1). (Thanks to K.
Mawatari.)
- p. 368: In the first line of the second paragraph, "V(phi)" should read
"V(phi_cl)". (Thanks to K. Mawatari.)
- p. 369: The vertical axis of the figures 11.6 and 11.7 should be
labeled "V_eff". (Thanks to K. Mawatari.)
- p. 385: In eq. (11.99), the large parenthesis surrounding the
integrand should not include "+1/2 log det(-iD)". (Thanks to K. Mawatari.)
- p. 369: The vertical axis of the figures 11.6 and 11.7 should be
labeled "V_eff". (Thanks to K. Mawatari.)
- p. 371: In eq. (11.60), "-i" should be simply "i". (Thanks to
K. Arai.)
- p. 373: Just below eq. (11.66), "According to Eq. (11.63) should
read "According to Eq. (11.64)". Also, in eq. (11.67), the left-hand side
should be evaluated at phi = phi_cl. (Thanks to S. H. Jung.)
- p. 382: In the unnumbered equation in the middle of the page,
the denominator of the left-hand side should read: "delta phi_cl(x)
delta phi_cl(y) delta phi_cl(z)" (Thanks to M. Yamada.)
phi_cl(z)".
eq. (11.100), we should have stated explicitly that the
quadratic form D^{ij} is to be evaluated at phi_c(x). (Thanks to C. Locke.)
- p. 385: In eq. (11.99), the first term in the integral should
be:
"1/2 (del_\mu \phi_cl^i)^2" , not "\del_\mu^2". (Thanks to C. Zhang.)
- p. 385: In eq. (11.100), we should have stated explicitly that the
quadratic form D^{ij} is to be evaluated at phi_c(x). (Thanks to
C. Locke.)
Chapter 12:
- p. 402: In the line just below eq. (12.27), "Notice that the coefficient"
should be replaced by "Notice that the exponent". (Thanks to
S. Groote.)
- p. 416: In the unnumbered equation at the top of the page,
"gamma^mu" should be "gamma^nu" and the indices mu and nu in the
projector "(g_mu nu -q_mu q_nu/q^2)" should be lowered. (Thanks to
M. Yuan).
- p. 421: Just above eq. (12.77), the condition should read: "evaluated
at spacelike momenta p_i such that p_i^2 = -P^2 and all three invariants
s, t, and u are of the order of -P^2." (Thanks to S. Gubser.)
- p. 430: The right-hand side of eq. (12.110) should read " {1/2}
\bar\psi [ gamma^mu D^nu + gamma^nu D^mu] psi - F^{mu
lambda}F^nu_lambda + (1/4) (F_{mu nu})^2 ". You will find the
energy-momentum tensor of QED given correctly later in the book in
eq. (19.150). (Thanks to G. Johnson.)
- p. 435: In the second and third lines below eq. (12.131), "the
omitted correction terms are of order lambda (d-4)" should be replaced
by " ... lambda^2 (d-4)". (Thanks to M. P. Le).
Chapter 13:
- p. 442: In Eq. (13.13), on the right-hand side, "rho_j"
should read "\bar rho_j". (Thanks to S. Kos.)
- p. 444: In Eq. (13.20), the prefactor on the right-hand side should be "-i", not "i",
for consistency with Eq. (11.96). Eq. (13.21) is correct. These
normalizations do not affect the argument that follows. (Thanks to
P. Axolotl.)
- p, 459: In Eq. (13.92), the third term in the bracket should be
" 2 (phi_a del^mu phi_b)(e_b del_mu e_a)" . The first term in the
bracket in the second line should be " 2 del^mu phi_a del_mu n . e_a
". These terms do not contribute to Eq. (13.97), so they do not
affect the final answer. (Thanks to P. Axolotl.)
- p. 461: In the paragraph below Eq. (13.106), lines 4 and 5, the
variable "t" should read "T". (Thanks to S. Kos.)
- p. 462: Eq. (13.107) should read: "eta = 2 gamma(T_*) =
(N-1) epsilon/(M-2)". (Thanks to S. Osamu.)
- p. 464: In Eq. (13.121), "beta(g^2)" should read "beta(g)"
(Thanks to Petra Axolotl.)
- p. 465: Eq. (13.124) has several errors. The equation should
read: " C_1 = [ 2^{d-1} pi^{d/2} Gamma(d/2) (d-2) ]^{-1} ". (Thanks
to Petra Axolotl.)
- p. 465: In eq. (13.127), on the left-hand side, in the
denominator, "g_C^4" should
read "g_C^2". (Thanks to Petra Axolotl.)
- p. 466: In Problem 13.2, there is not an error, but there is an
unexpected subtlety. The value for gamma given in this problem is
correct for phi^4 theory with the interaction term 1/4! lambda phi^4.
However, the value of gamma given in eq. (13.47) is correct for the
N-component scalar field theory, for which we use the interaction term
1/4 lambda (phi^2)^2. See pp. 348-49 for a presentation of these
conventions. (Thanks to D. Renner.)
Chapter 14:
Chapter 15:
- p. 482: In the 4th line under eq. (15.2), "tranformation" should
read "transformation". (Thanks to N. Yamanaka.)
- p. 492: In the footnote, David Bohm's name has no umlaut.
(Thanks to H. Dreiner.)
- p. 493: Just below eq. (15.60), "right-hand side" should read
"left-hand side". (Thanks to A. Virmani.)
- p. 503: In the equation in Problem 15.3, part (c), the quantity
in brackets on the left-hand
side should read "A^a_mu (x) A^b_nu(y)". (Thanks to E. Schemm.)
Chapter 16:
- p. 508: It might be good to be a little more explicit about
where the indices go in eq. (16.11). The spinors u(p) and v(p+) are
the usual 4-component Dirac spinors. The gamma matrices act on
these. The matrices t^a, t^b act in the gauge or color space. In QCD, these
would be 3x3 matrices. The color vectors for the initial fermion and
antifermion (3-component complex vectors for QCD) are not written
explicitly. Rather, we consider M to be a 3x3 matrix in color
space, to be evaluated later between color wavefunctions. Usually,
we will square M and sum or average over colors.
This will give a trace over the t^a matrices that can be evaluated
using methods from Chapter 15. (Thanks to T. Wettig.)
- p. 511: The expressions for polarization vectors given in eq.
(16.18) are those for epsilon^{+ mu} and epsilon^{ - mu},
that is, for the vectors with raised indices. (Thanks to
H. Logan.)
- p. 529: In the equation at the top of the page, the last line
of eq. (16.76), the expression on the right-hand side should be
multiplied by "1/(k^2)^{2-d/2}". This gives the denominator of
eq. (16.77), which is correct. (Thanks to G. Piazza.)
- p. 532: In eq. (16.87), in the second line, "psibar gamma^mu
psi" should be "psibar gamma^mu t^a psi". (Thanks to R. Schabinger.)
- p. 532: The list of counterterms for the non-Abelian gauge theory
should include a term "delta_xi (del^\mu A_\mu)^2" associated with
a change of gauge. Since the vacuum polarization is transverse, the
loop corrections, in general, change the gauge. To work in a fixed gauge,
we need a counterterm to correct this effect. (Thanks to A. Nelson.)
- p. 535: In eq. (16.98), the "*" in the first line should be a "+".
(Thanks to R. Schabinger.)
- p. 539: In eq. (16.121) "gamma^{mu nu}" should read "g^{mu nu}".
(Thanks to Lijun Zhu.)
- p. 539-40: In eqs. (16.121), (16.125), and (16.129) "A_mu^a
A_nu^b" should read "A_mu^a A_nu^a".
(Thanks to P. Axolotl.)
Chapter 17:
- p. 551: Just after eq. (17.11), "were" should read "where".
(Thanks to S. Salinger.)
- p. 552: In eq. (17.15), "+ +" should read simply "+". (Thanks to
T. Azuma.)
- p. 559: The weak-interaction effective Lagrangian given in
eq. (17.31) should have a minus sign "-" in front
of them. (Thanks to S. Martin, who points out that this error has
propagated acausally from eq. (20.90).)
- p. 562: In eq. (17.37), at the end of the line, "f_{dbar}" should
read "f_dbar(x)". (Thanks to M. Yamada.)
- p. 563: In the second line of Section 17.4, "cosituent" should read
"constituent". (Thanks to A. Mariano.)
- p. 575: In the third line of the second paragraph, "tranfer" should be
"transfer". (Thanks to J. Vollinga.)
- p. 583: In eq. (17.111), both lines, the factor
"f_e(x',p_perp)" should be evaluated at p_perp = Q and written as
"f_e(x',Q)".
(Thanks to S. U. Min.)
- p. 597: In problem 17.3, part (b), the text below the second
unnumbered equation should read "... only six of the 16 polarized gluon
scattering cross sections are nonzero." These are the six cross sections
that are derived by crossing gR gR-> gR gR. (Thanks to R. Schabinger.)
Chapter 18:
- p. 603: In eq. (18.19), the symbol "m" in the middle expression should
be "\bar m". (Thanks to M. Yamada.)
- p. 605: The weak-interaction effective Lagrangian given in
eq. (18.27) should have a minus sign "-" in front
of them. This changes the overall sign of all effective Lagrangians
given in Section 18.2.
(Thanks to S. Martin, who points out that this error has
propagated acausally from eq. (20.90).)
- p. 610: In the first line of text after eq. (18.55), "than"
should read "that". (Thanks to T. van Daal.)
- p. 616: In eq. (18.80), the prefactor "1/2s" on the right-hand
side should read "1/s". The other factor of 2 is supplied by the
fact that the left-hand side of eq. (7.49) is equal to 2 Im
M(a->b). This error is corrected in the rest of the derivation
leading to eq. (18.84). (Thanks to C. Sun.)
- p. 618: In eq. (18.94), the prefactor on the right-hand side should
read "4 PI alpha/s" (not "alpha^2"). (Thanks to Y. Wu.)
- p. 626: A factor "Q_f^2" is missing in eqs. (18.117) and
(18.118). It is restored in eq. (18.119). (Thanks to T. van Daal.)
- p. 629: In eq. (8.131), the index "mu_k" should be "mu_n". (Thanks to T. van Daal.)
- p. 635: In eqs. (18.157) and (18.158), the parton distribution
functions "f^-" and "f^+" should carry the subscript $f$. (Thanks to T. van Daal.)
- p. 637: Just above the final equation (18.168), "Fig. 18.3"
should read "Fig. 18.13". (Thanks to T. van Daal.)
- p. 641: In eq. (18.184), the mysterious comma on the left-hand
side should be omitted. (Thanks to T. van Daal.)
- p. 645: In eq. (18.200), the subscript "nf" should read "fn".
(Thanks to T. van Daal.)
Chapter 19:
- p. 658: Two lines above eq. (19.37), "adiabiatically" should read
"adiabatically" (Thanks to N. Yamanaka.)
- p. 658: In eq. (19.38), the expression in parentheses on the
left-hand side should read "( (e/2 pi) epsilon^{mu nu} F_{mu nu})
". The right-hand side of the equation is correct.
(Thanks to S. Baek.)
- p. 662: Just below eq. (19.49), "pass gamma^nu through gamma^5"
should read "pass gamma^lambda through gamma^5". (Thanks to
K. Kumericki.)
- p. 663: In eq. (19.54), the momenta p and k are switched with
respect to eq. (19.48). Actually, this does not change the value of
the expression, but it is very confusing. So, please change back
(ell+k) -> (ell+p) and (ell-p) -> (ell-k), so that the first two terms
on the right hand side of (19.54) are identical to the two terms on
the right-hand
side of (19.48). (Thanks to F. Marino.)
- p. 666: Equation (19.74) should read : (iDslash)^2 = - D^2 -
(e/2) sigma^munu F_munu ; that is, the sign in the second term
should be changed. This equation is copied from eq. (16.107), but
Chapter 16 uses a different convention for the covariant derivative
from Chapter 19. In Chapter 16, D_mu = (del_mu - ig A_mu) -- as
for gauge theories -- while in Chapter 19, D_mu = (del_mu +ie A_mu)
-- as for QED. This wrong sign cancels out of (19.75) and below,
but the sign of (19.80) should be changed to (-1)^n. Please check
your conventions carefully before using the anomaly equations (or
any equations involving the epsilon_abcd symbol). (Thanks to A. Brook-Ray.)
- p. 675: In eq. (19.117), the quantity on the right-hand side should
be multiplied by (-1). This sign does not affect the discussion that
follows on p. 676. (Thanks to Q. Chang.)
- p. 683: The should be a minus sign in front of the right-hand side
of eq. (19.148), since del g^mn /del(g_pq) = - g^mp g^qn. Fortunately,
this sign
does not play a role in the later parts of this section. (Thanks to M.
Noorbala.)
- p. 683: In eq. (19.151), the term "+m" in the second parentheses
should read
" + gamma^0 m ". (Thanks to M. Yamada.)
- p. 683: In eq. (19.151), the term "gamma^0 \vec \gamma \cdot
\vec \nabla" should read "gamma^0 \vec \gamma \cdot
\vec D". Note that this term generates a vertex that is used in the
second diagram in Fig. 19.10. and the associated calculation. (Thanks
to B. Armstrong.)
- p. 684-686: There is no error here, but readers should be
careful to note that, just above eq. (19.156), the A field is
rescaled by e A_mu -> A_mu. From here until the end of chapter, we
are using the convention in which e is scaled out of the covariant
derivative and instead appears in front of the (F_mu nu)^2 term as
in eq. (19.156). This convention is not used elsewhere in the book,
except in Section 16.6. The results of this section for the trace
anomaly in QED would appear
in the more usual convention with (F_mu nu)^2 multiplied by a factor
of e^2. (Thanks to S. Davidson.)
- p. 686-7: In Problem 19.1, there are a number of errors. In
part (a), the right-hand side should have a + sign, ie, the
prefactor should be (+ e^2/2pi^2). In part (b), below the
equation,
{\bf D} should be equal
to ( del_i + i e A_i) or {\bf D } = ( del_i - ie A^i) . In
part (e), the sentences beginning in line 2 should read: "Show that
the vacuum gains right-handed fermions. Repeating this analysis for
the left-handed spectrum, one sees that the vacuum loses the same
number of left-handed fermions." Now everything works out
correctly. (Thanks to R.-H. Fang.)
Chapter 20:
- p. 707: Figure 20.2 might also have included anomaly diagrams with
one SU(2) boson and two gravitons or one SU(3) boson and two gravitons.
However, these anomalies are zero by eq. (20.82). (Thanks to
Y. Wu.)
- p. 708-9: The weak-interaction effective Lagrangians given in
eqs. (20.90), (20.92), (20.94) should have a minus sign "-" in front
of them. (Thanks to S. Martin.)
Chapter 21:
- p. 749: Equation (21.79) should read "phi^\pm = 1/sqrt{2} (phi^1
\mp i phi^2)", where \pm = + over - and \mp = - over +. It is the
phi^- field that creates the Goldstone boson phi^+. Then eq. (21.80
should read "delta L = i lambda_t bbar_L (phi^+)^dagger t_R" and
eq. (21.81) should have an extra -i, leading to "i M = -lambda_t
ubar (1+gamma^5)/2 u$". The results below this equation are
unchanged. (Thanks to
T. Toma and E. Christiansen.)
- p. 751: In eq. (21.89), the last expression in the formula
should read "s / 2 m_W^2". (Thanks to A. Levin.)
- p. 761: In eq. (21.115), on the right-hand side, "Delta(q^2)"
should read "Delta_{IJ}(q^2)". (Thanks to T. Toma.)
Chapter 22:
Index:
- p. 818: In the second entry on the page, the name is correctly
spelled "Bogoliubov". (Thanks to L. Fillion.)
- p. 828: Under "Infrared divergences", the reference to p. 55 is
an error and should be removed. (Thanks to L. Fillion.)
- p. 831: Under "Momentum conservation in diagrams", the reference
should be to p. 94. Under "Negative energy", the reference to p. 54
should be to p. 55. (Thanks to L. Fillion.)
- p. 831: The index item for "Negative frequency" should read
"Negative frequency, 26,48" (Thanks to L. Fillion.)
- p. 834: The index item for "Positive frequency" should read
"Positive frequency, 26, 45, 48" (Thanks to L. Fillion.)
- p. 840: Under "Ultraviolet divergences", a reference to p. 176
should be added. (Thanks to L. Fillion.)
- p. 841: For "Vacuum polarization", the entry should read:
Vacuum polarization, 176, 244; see also $\Pi(q^2)$, ... (Thanks to L. Fillion.)
Errata for Zhong-Zhi Xianyu's solutions to the problems:
- p. 200: Because the Final Project for Part III is a problem
set, it omits some important features of the full computation of the
Higgs boson partial widths. The discussion of h->WW and h-> ZZ is
particularly oversimplified. The current definitive treatment of
the Higgs boson partial widths can be found in the "Handbook of LHC Higgs
Cross Sections: 3. Higgs Properties", by the LHC Higgs Cross Section
Working Group, arXiv:1307.1347.
See especially Figure 2 (p. 5) and Tables
A.1-14 (pp. 265-278).
The Book
M. E. Peskin
SLAC
