#  Fourth Edition Corrections 

 



This page lists corrections to the **third or fourth printing**    
(reads "3rd printing 2015" or "4th printing 2015" on imprint page)

## Important corrections (Errors in derivations or results)

None so far.

## Minor corrections (Unimportant errors in equations)

p. 20, Eq. (2.65): There should be a factor of volume “V” multiplying the “½” in the Hamiltonian. Same correction applies to Eqs. (2.79), (2.96), (15.3) and (15.4).   
p. 49, Eq (4.16): The factors of “e” should not be there in any of the terms.   
p. 50, Eq (4.18): The factor of “e/2” after the first = sign should not be there.   
p. 60, Eq. (5.17): Left-hand side should be "<f|T|i>" not just “T”.   
p. 60, Eq. (5.18): Right-hand side should have “M” not “<f|M|i>”.   
p. 65, Eq. (5.44): right hand side should be “<s3 s4|ε><ε|s1 s2>” instead of “<s1 s2|ε><ε|s3 s4>”.   
p. 66, Eq. (5.50) and (5.51): These equations should be corrected as follows:

SortReads in third printing:



Should read:







p. 138, Problem 8.4: This problem is extremely difficult. See Greiner and Reinhardt “Field Quantization” chapter 7 for a solution. A more reasonable problem is to calculate the propagator for a photon in a physical gauge, such as axial gauge, A0 = 0.   
p. 149 Eq. (9.42) and p. 150 Eqs. (9.44) and (9.45): There is a missing factor of (2π)4 on the right-hand side of all of these equations.   
p. 179, Eq. (10.131): The matrix in this equation should be negated to be consistent with Eq. (10.134). That is, the top row should be 0 -1 and the bottom row 1 0.   
p. 180, Eq. (10.133): The last term should have a minus sign “=-i ψα εαβ ψβ”. Also, in the line below there is an extra minus sign. It should be “εαβ = iσ2αβ” instead of “εαβ =−iσ2αβ”.   
p. 181, Problem 10.1(b): The expression “(HD + e A0)2” should be “(HD - e A0)2”.   
p. 187: In the definition of helicity, the helicity eigenstates have eigenvalue ±S not ±1.   
p. 196, Discussion of intrinsic parities in Section 11.5.1 could be clearer. [Here](http://www.schwartzqft.com/parity.pdf) is a revised discussion.   
p. 199, Eq. (11.74): In the next to last expression, where the minus sign is introduced, the α and γ subscripts should be interchanged.   
p. 201, Fist line below Eq. (11.90): There should be a minus sign in the transformation of Aμ. That is, CPT sends, Aμ(x) -> - Aμ(-x).   
p. 201, Eq. (11.91): There should be no i in the ψAψ term.   
p. 221, Eq. (12.81): There should be no factor of “i” in the definition of D1 on the last line.   
p. 264, Eq. (14.62): There is a missing factor of “Z0\[0\]” on both terms on the right hand side of the first equality. That is, “1/Z\[0\]” should be “Z0\[0\]/Z\[0\]” in two places.   
p. 278, Eq. (14.132): The “+m” in the Dirac Lagrangian should be “-m”.   
p. 278, First line below Eq. (14.132): “... represent any globally symmetric terms.” should be “... represent any locally symmetric terms.”.   
p. 283 Problem 14.1: The left-hand side of this equation is not right. It should read:

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Should read:







p. 301, 3rd line of paragraph beginning “In Section 15.4…”: The inline equation should be “< φ4 > = − λ − ..” rather than “< φ 4 > = λ− ..”.   
p. 308: Factors of iε missing in Eqs. (16.41) and (16.44).   
p. 314, Problem 16.3c: This problem should be asking about the total rate for π+π- → τ+τ- not π+π- → e+e-.   
p. 318, Eq. (17.13): In the second and third diagrams the arrow on the fermion in the loop is pointing the wrong way.   
p. 324, First paragraph: The diagrams vanish, but not because there are an odd number of γ matrices. More simply, they must be proportional to the photon momentum, but Lorentz invariance (it is the only 4-vector around), but this momentum must vanish, by momentum conservation.   
p. 336, First line on page: “with residue i” should not be there.   
p. 344, First line after Eq. (19.34): There is an extra factor of p4 in the definition of Π(p2). The line should read: “Π(p2) is defined as the coefficient of i/p2 (-g μν − pμ pν/p2)” as it is on p. 349, second paragraph.   
p. 346, Eq. (19.43): me should be mR.   
p. 362, Eq. (20.44): Tr \[ q1 S q2 S\] should be Tr\[ p3 S p4 S\], as in Eq. (20.43).   
p. 402, Eq. (22.19): There should be no dagger on the last term.   
p. 402, Eq. (22.20): The coefficient on the second term on the right-hand side shuold be 4/45 not 1/18.   
p. 419: Eq. (23.3): The numerator on the right hand side should have written “eR2Π(p2) + δ3” instead of “eR2Π(p2)”.   
p. 427, Eq. (23.31): The power of the β2 term should be 3, not 2.   
p. 413, Eq. (22.59): m and M should be switched in the denominators on the second line.   
p. 447, Fig. 23.2: The x-axis in the figure should have positive numbers (0.5, 0.55, etc.). Also the caption should read “... the value of λ6 (ΛL) goes to a constant value, entirely set by λ4 (ΛL) … “ instead of “... the value of λ6 (Λ) goes to a constant value, entirely set by λ4 (Λ) … “.   
p. 457, Eq. (24.30): There is a missing factor of “i” on the left-hand side (“M” should be “i M”). Eq. (24.31) still follows, as it is the imaginary part of i times the Feynman propagator to which Eq. (24.25) applies.   
p. 458, Eq. (24.34): There is a missing factor of (2π)4 on the right-hand side.   
p. 459, Eq. (24.39): A factor of (2π)4δ4(p - q1 - q2)” is missing from the right-hand side.   
p. 459, Eq. (24.40): The first factor of “δ(q22)” should be “δ(q12)”   
p. 471, Eq. (24.85): The first line should be evaluated at t=0 after the derivative is taken.   
p. 471, Eq. (24.86): The left hand side should be integrated over x, rather than p. That is

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Should read:







p. 484, last paragraph on page: “For SU(N), the fundamental representation is the set of the N x N Hermitian matrices with determinant 1.” should be “ For su(N), the fundamental representation is the set of the N x N Hermitian matrices with trace 0.”   
pp. 503-505: All instances of “N” should be “n” in this section. That is, W(N) should be W(n), A(N) should be A(n), etc.. The exception is the factor of N in the denominator in Eqs. (25.133) and (25.134) which are N= Nc, the number of colors. These N’s really are N’s.   
p. 505, Eq. (25.135): There is a missing “=” sign between “C(x)” and “<Ω | … “.   
p. 511, Eq. (26.14): The Feynman rule should have an anticommutator. That is:

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Should read:







p. 515, Above Eq. (25.27): Summing over colors gives Tr\[TaTa\] = N CF, not just CF as written. The extra factor of N is already included in the sum over colors at tree-level, so Eq. (26.27) is correct.   
p. 524, Eq. (26.70): The -½ on the first line should be a -1, as in Eq. (19.54).   
p. 527, Eq. (26.96): The exponent on the β3 term should be 4, not 3.   
p. 532: The factors of “i E T” on the left-hand sides of Eqs. (26.113), (26.114) and (26.116) should be “- i E T”. The “e i H T” factor in Eq. (26.113) should be “e -i H T”. Also, below Eq. (26.116), it should be “E = - e2/4πR = V(R)” instead of “E = e2/4πR = V(R)”.   
p. 538, Eq. (27.19): The σ’s in this equation should be barred.   
p. 571, Eq. (28.31): One of the currents should have †. That is, “JμLJμL” should be “JμL†JμL”.   
p. 571, Eq. (28.32): In the second term on the right-hand side, “γμγ5” should be “γμ (1-γ5)”.   
p. 571, 4th line after Eq. (28.35): The transformation law for M should be “M → gR M gL†” instead of “M → gL M gR†”.   
p. 581, Eq. (28.62): The left hand side should have “G\[Aμ + Dμ, π − α\]” instead o f “G\[Aμ - Dμ, π − α\]”. Also, on the right-hand side, “mA” should be squared in both instances.   
p. 581, Eq. (28.64): The sign of the ghost mass term is wrong. The expression “-ξ mA2” in the last term should be “+ξ mA2”   
p. 586, Eq. (29.9): There is a factor of 2 missing and a few signs are wrong. Correction as follows:

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Should read:







p. 590, Eq. (29.27): The 1/v should be v.   
p. 591, Eq. (29.28): “v2” on the right should be “½ v2”.   
p. 591, Eq (29.32): The “(t-mh2)” term in the denominator on the far right-hand side should not be squared.   
p. 593, Eq. (29.36): The “g” on the far right on the first line, multiplying “YL B” should be a “g’”.   
p. 600, Above Eq. (29.64): The expression for “ψR” should have a minus sign in the top component: “ψR = ( −iσ2 νR\* , νR)”.   
p. 604, Eq. (29.78): The fermions should have “L” superscripts in the first term in square brackets on the right-hand side.   
p. 605, Second line: The process listed should be “s -> d e+e-”.   
p. 605, Eq. (29.81): T3 was not applied. Correction as follows:

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Should read:







p. 607, Eq. (29.90): There should be no overall minus sign on the right-hand side.   
p. 612, Eq. (29.109): The middle expression is incorrect. Instead of the factor of “2 ms” in the numerator, there should be a factor of “(2ms - mu - md)” in the denominator.   
p. 627, Eq. (30.53): The “ 1/2 (QR3 - QL3 ) M5αμν” term on the right-hand side should have “ 1/2 (QR3+ QL3 ) MVαμν” added to it.   
p. 635, second paragraph: The last two sentences from this paragraph, “If such a gauge boson exists ... be very heavy (> 1016 GeV).” should be deleted.   
p. 636, paragraph after Eq. (30.89), next to last line: The current experimental bound on the strong CP phase is “θ < 10−10”, not “θ < 10−12”.   
p. 637, Eq. (30.93): The “a” superscripts on the last two F’s should be “b”’s.   
p. 654, Eq. (31.74): The right hand side should have “J3 - s2 JEM” instead of “J3 + s2 JEM.   
p. 659, Eq. (31.87): The left-hand side should be “i M” not just “M”.   
pp. 712-732. There were a number of sign errors and small typos in Sections 3.4, 3.5 and Appendix A of Chapter 33. Rather than list them all, I provide the corrected complete Chapter 33 in [this pdf file](http://www.schwartzqft.com/Chapter33.pdf).   
p. 764, two lines above Eq. (35.19): It should read “depend on the combination w = v · v’ ” instead of “depend on the combination w = v · v ” (missing prime on v).   
p. 820, Eq. (A.42): The indices on the right hand side should be μναβ in order, as on the right-hand side.   
p. 832, Eq. (B.60): In the second line of this equation, the denominators should have + signs, not - signs. That is, they should be “(kE2 + m2)2” and “(kE2 + Λ2)2”.

## Typos (Superficial formatting issues)

p. 58, below Eq. (5.4): L is the “integrated luminosity” not the “luminosity”.   
p. 114: First paragraph of Section 8.2.2, “4 = 3 ⊕ 1” should be “4 = 1 ⊕ 0” and at bottom of page “4 = 1⊕1⊕1⊕1” should be “4 = 0⊕0⊕0⊕0”.   
p. 115, paragraph afater Eq. (8.20): “4 = 3 ⊕ 1 instead of 4 = 1 ⊕ 1 ⊕ 1 ⊕ 1” should be “4 = 1 ⊕ 0 instead of 4 = 0 ⊕ 0 ⊕ 0 ⊕ 0”.   
p. 136, Eq. (8.139): The “v” on the second line should be a “ν”.   
p. 142, after Eq. (9.10): “Fermi exclusion principle” should be “Pauli exclusion principle”.   
p. 160, Eq. (10.13): The summation symbol should be outside the square brackets.  
p. 163, Table 10.1: “describing” is misspelt.   
p. 180, Eq. (10.133): The “a” in “εaβ” should be an “α”.   
p. 182, Problem 10.1(f): There should be no arrow on top of H on the first line of the page.   
p. 182, Problem 10.1(h), 4th line: “... are all me times powers …” should be “... are all me-1 times powers …”. Also “time-dependent” should be “time-independent”.   
p. 182, Problem 10.2(b): the equation “λmax = j” should be “λmax = J”. Also, at the end of the introduction to the problem, “τ± = τ1 ± iτ 2” should be “τ± = τ1 ± i τ 2”.   
p. 191. Eq. (11.32): The \* on the first epsilon should be removed.   
p. 200, Eq. (11.83): The bar over the x on the left hand side should be an arrow.   
p. 201, Eq. (11.91): The last term (ψσμνψFμν ) should not have an “i”.   
p. 202, Problem 11.6. This problem has generated some confusion. A cleaner version would be: (a) Use the left and right chirality projection operators to show that the QED vertex vanishes unless ψ and its conjugate are both left-handed or both right-handed. And (d) Suppose we take a spin-up electron going in the +z direction and turn it around carefully with electric fields so that now it goes in the -z direction but is still spin up. Has its helicity or chirality flipped (or both)? How is your answer consistent with part (a)?   
p. 218, Eqs. (12.66), (12.67) and (12.68): The “d3q” should be replaced by “d3p”.   
p. 249, Problem 13.6(d): Ni59 should be Ni60 in two places (as in Problem 11.6(f) on p. 202). Also, C (Carbon) should be Co (Cobalt).   
p. 258, Eq. (14.27): The integration measure “d” should be “D” on the second line.   
p. 280, Eq. (14.146), The “p” in the argument of M on the left hand side should be omitted.   
p. 296, Eq. (15.57): there is a superfluous “m” on the diagram that should not be there.   
p. 305, Eq. (15.1): the lines in the loop should be dashed since they are scalars not fermions.   
p. 310, First line of Section 16.3.1: “|p2| << m” should be “|p2| << m2”.   
p. 315, Above Eq. (17.2): Missing parenthesis. "i Dslash - m)" should be "(i Dslash - m)".   
p. 321, Problem 17.1 (b): The values for (g-2)/2 have the decimal place in the wrong spot. 0.0011659208 and 0.0011659182 for the experiment and theory values, respectively. The uncertainties are correct.   
p. 322, Second paragraph, 4th line: “ logarithmic weakening of the Coulomb potential at large distances” should be “ logarithmic strengthening of the Coulomb potential at short distances.”   
p. 327, Below Eq. (18.14): Reference to Chapter 9 should be a reference to Chapter 16.   
p. 332, Line below Eq. (18.42): Only condition (18.40) is required to define the pole mass.   
p. 339, Third paragraph: reference to Chapter 15 should be to Chapter 16.   
p. 339, Eq. (19.1): The first ψ should have a bar over it.   
p. 345, Five lines before Eq. (19.39): δ3 should be δ1.   
p. 353, Below Eq. (19.82): F1 (0) = 1 sets δ1 and Σ′ (mR)=0 sets δ2, not vice versa as written.   
p. 460, Eq. (24.44): The μ and ν indices on the final two p’s should be interchanged. Also, the sum on the left hand side should be over i and the second epsilon should have a ν index.   
p. 502, Second line below Eq. (25.120): It should read “rμΠμνabaxial = 0”. The “=0” is missing.   
p. 566, Eq. (28.15): The variation should be ∂L/ ∂(∂μ π) instead of just ∂L/∂μ π.   
p. 571, Eq. (28.33) and the line above Eq. (28.33): It should be “π → μ νμ” not “π → μ νe” in both cases (as in Eq. (23.34)).   
p. 582, 5th line from bottom: “E>> m2” should be “E>> m”.   
p. 602, Third paragraph: Reactor neutrinos are mostly electron anti-neutrinos and accelerator neutrinos are mostly muon neutrinos (not the other way around, as written).   
p. 603, above Eq. (29.69): The W- is missing a μ index.   
p. 603, Eq. (29.70): There is an extra j on the τ neutrino (third term on the right-hand side).   
p. 603, Eq. (29.74): One of the neutrinos should be an anti-neutrino.   
p. 612, line after Eq. (29.111): There is an extra |dN|. That is, “|dN| < |dN| < 2.9 x 10-26 …” should be simply “|dN| < 2.9 x 10-26 …”.   
p. 614, Last paragraph: Maximal means δ = π/2 not δ = π as written.   
p. 633, Eq. (30.79): The “A(R)dabc” on the right hand side should be “½ A(R)dabc”.   
p. 760, Footnote: “phase” should be “phrase”.

## Credits

  
**Minor correction on p. 49, 50: Thanks to Sho.**  
  
**Minor correction on p. 66: Thanks to Ted.**  
**Minor correction on p. 138, Thanks to Stefano.**  
**Minor correction on p. 149, Thanks to Ken.**  
**Minor correction on p. 179, Thanks to Luca.**  
**Minor correction on p. 180, Thanks to Chi.**  
**Minor correction on p. 181, Thanks to Heshy.**  
**Minor correction on p. 187,199 Thanks to George.**  
**Minor corrections on p. 201, Thanks to Oliver.**  
**Minor corrections on p. 221, Thanks to Hongbin.**  
**Minor correction on p. 264, Thanks to Allan.**  
**Minor correction on p. 278, 336 Thanks to Enrico.**  
**Minor correction on p. 278, Thanks to Sahand.**  
**Minor correction on p. 318, Thanks to Dan.**  
**Minor correction on p. 324, Thanks to Christopher.**  
**Minor correction on p. 344, 346 Thanks to Andrea.**  
**Minor correction on p. 380, 447, 471, 503-505, 524, 532. 538, 591, 593, 600, 605, 633, 637 Thanks to YoonSeok.**  
**Minor correction on p. 427, Thanks to Jeff.**  
**Minor corrections on p. 301, 457, 458, 459, Thanks to Ken.**  
**Minor correction on p. 402, 425 Thanks to Dmitry.**  
**Minor correction on p. 427 Thanks to Andrea.**  
**Minor correction on p. 505 Thanks to Yidun.**  
**Minor correction on p. 515, 590 Thanks to Joon.**  
**Minor corrections on p. 571, 581 Thanks to Yoon.**  
**Minor correction on p. 591, Thanks to Jong.**  
**Minor correction on p. 591, Thanks to Wim.**  
**Minor correction on p. 612, Thanks to Kit.**  
**Minor correction on p. 635, Thanks to Michael.**  
**Minor correction on p. 636, Thanks to Johar.**  
**Minor correction on p. 654, Thanks to Kaushuk.**  
**Minor correction on p. 659, Thanks to Christian.**  
**Minor correction on p. 764, Thanks to Matthias.**  
**Minor correction on p. 820, Thanks to Wim.**  
**Minor correction on p. 832, Thanks to Kari.**  
  
**Typo on p. 180, Thanks to Tianhong.**  
**Typo on p. 136, 191, 200, 201, 460, Thanks to Ken.**  
**Typo on p. 160, 258, Thanks to Andrea.**  
**Typo on p. 163, 182, 315, 339: Thanks to Eric.**  
**Typo on p. 180, Thanks to Luca.**  
**Typo on p. 182, Thanks to Guyjin.**  
**Typo on p. 218, 280: Thanks to Sahand.**  
**Typo on p. 305, Thanks to Jose.**  
**Typo on p. 310, 321 Thanks to Kari.**  
**Typo on p. 329, Thanks to Scott.**  
**Typo on p. 332, Thanks to Enrico.**  
**Typo on p. 339, Thanks to Kevin.**  
**Typo on p. 353, Thanks to Michele.**  
**Typo on p. 413, 502, 582. Thanks to YoonSeok.**  
**Typo on p. 460, Thanks to Yair.**  
**Typo on p. 566, Thanks to Jong.**  
**Typo on p. 589, Thanks to Fotis.**  
**Typo on p. 602, Thanks to Gleb.**  
**Typo on p. 603, Thanks to Matthias.**  
**Typo on p. 712, Thanks to Guy.**  
**Typo on p. 760, Thanks to Eric.**