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Department of Physics

# Errata

When you find errors in the book we would be grateful if they could be emailed to tom.lancaster_at_durham.ac.uk. Corrections to the exercises may be found here.

### Corrections to the scientific content

We recommend that you correct the following errors in your copy of the book.

#### Corrections to the third reprinted edition (May 2016)

These errors occur in the first printings and the first three corrected reprints (the last dated May 2016). They are corrected in the fourth corrected reprint, which can be identified by the note dated November 2017 that has been added to the Preface.

• Page 26, eqn 2.66: the sum should be over k, taking values 2πm/Na, where m in an integer in the range -N/2 < mN/2. Note that the convention is to exclude one of the end points if the number of atoms N happens to be even. (11/08/17)
• Page 52, example 5.2, equation (5.20): in the second term on the RHS of the first line, the indices in the numerator quantities should be swapped, i.e. pj becomes pk and qk becomes qj. (03/08/17)
• Page 107: line before eqn (11.49): the subscript on the energy should be q rather than p. (03/08/17)
• Page 129, eqn (14.12): the final Aμ, should be an Aμ. (03/08/17)
• Page 132, two lines after eqn (14.28): insert minus sign on right hand side. In eqn (14.29) the j operator should sit on the left of the delta function, so the RHS reads i j δ(3)(x-y). (08/08/17)
• Page 173, eqn 18.38: Insert a time-ordering symbol on the left hand side. (10/08/17)
• Page 178, second line of eqn 19.10: add two time-ordering symbols. (10/08/17)
• Page 180 eqn (180): change a_\matbf{p} to a_\mathbf{q}. (10/08/17)

• Page 184, Fig. 19.8: these are note quite all of the phi4 diagrams. One is missing that contains (i) a line and (ii) a part resembling an eye, fromed from two points joined with four lines. (10/08/17)
• Page 184, eqn (19.19) is missing the integral over w and y. (25/11/17)
• Page 185, example 19.7: diagram (f) is missing a factor (2π)4δ(4)(0). (13/08/17)
• Page 189 eqn (20.5) is missing the integral over w and y. (25/11/17)
• Page 197, eqn.(21.6) and two lines above it, the derivative should be evaluated at J=0, rather than Ji = 0. (03/08/17)
• Page 214, eqn (23.18): the lower limit of the integral is missing a minus sign. (25/11/17)
• Page 216, line after eqn (23.30): the constant should be (2π)N/2 (25/11/17)
• Page 218, eqn (23.41): replace ω=0 with ω0=0. (07/08/17)
• Page 222, line after eqn (24.5) the constant should be (2πi)N/2. (25/11/17)
• Page 224, line before Eq. (24.19): the square bracket should start before the integral sign, i.e. [∫...]^2. (04/08/17)
• Page 225, two lines before Example 24.4: change \mathcal{L} -> \mathcal{L}_0. (07/08/17)

• Page 232, sidenote 7: the expression at the end of the note should read ωn = (2n+1)π/β. (07/08/17)
• Page 247, third line of Section 27.1: replace 'ω' with 'ω/2'. In sidenote 1, remove factors of 1/2 from defintions of the operators P2 and Q2. (19/07/16)
• Page 258, eqn (28.23): the last term in the exponent should read \bar\psi(x)\eta(x). Equation (28.24) is missing an \int d^4 x \int d^4 y in the exponent. (04/08/17)

• Page 346, five lines before eqn (38.28): a ψ is missing before eiα(x). (04/08/17)
• Page 350, last Feynman rule: \epsilon^*_{\mu\lambda} -> \epsilon^*_{\nu\lambda}. (04/08/17)

• Page 360, last line of eqns (41.3): should read -iQ|e|. (07/08/17)
• Page 361, second line of eqn (41.5): g^{\mu\nu} -> g_{\mu\nu}. (04/08/17)
• Page 362 line after eqn (41.12): \Pi(q) -> \tilde\Pi(q)

• Page 408, example 44.6: in the definition of λ the quantity should be raised to the power 1/2 rather than -1/2. (03/08/17)

#### Corrections to the second reprinted edition (March 2015)

These errors occur in the first printings and the first two corrected reprints (the last dated March 2015). They are corrected in the third corrected reprint, which can be identified by the note dated May 2016 that has been added to the Preface.

• Page 38, side note refers to 4.13, but should refer to 4.12. (10/11/15)
• Pages 162, There is a missing time ordering operator T in the two equations for propagators in the text on this page. (07/06/15)
• Page 179, fifth line below eqn (19.14): there should be a |p> after (2Ep)1/2. (10/11/15)
• Page 183, eqn 19.18: HI(z) should be HI(w). (10/11/15)
• Page 189, eqn 20.4 and 20.5 are missing time ordering operators T. (07/06/15)
• Page 189, eqn 20.5: the final (i.e. right-most) ap operator in this expression should be ap. (05/05/15)
• Page 190: in Fig 20.2(a) the bubble contraction ψψshould be ψψ. Make the same swap for the bubbles in Fig. 20.3(a) and the line on the left in the oyster diagram in Fig 20.3(b). (07/06/15)
• Page 205, eqn (22.15): Disregard the sidenote and note instead that, for n>2 this sum excludes vacuum diagrams but includes those diagrams formed from products of diagram parts which are connected to the external lines. For example for n=4, we include products of two diagrams each with two external lines. (15/02/16)
• Page 212: line of text above eqn 23.8: delete the factor (2π) in the first expression for |qn>. (07/06/15)
• Page 222, eqn (24.3): the argument of the exponent on the right hand side is missing a factor 1/2 (30/04/16).
• Page 229, eqn (25.6): in the third equality the final superscript '2' should come after the |p| and before the closing bracket (i.e. the momentum is squared, rather than the sum of squared frequency and momentum.) (01/02/16)
• Page 234, eq (25.41): there should be an integral sign before the term on the left of the arrow. (10/11/15)
• Page 252, sidenote 11: the θ in the formula should be φ. (30/04/16)
• Page 262: The minima in Fig. 29.5 should be at v and -v for consistency with the text. (10/11/15)
• Page 278, first line below eq (31.9) the operator φ should have a dagger. (23/12/15)

• Page 284, Chapter Summary, bullet point 2: ε in the denominator of the propagator should be replaced by Γp
• Page 296, line below eqn 33.2: The operator φ(0) should be φ(0). (07/06/15)
• Page 307: the beta function for QED should read β = μ d|e|/dμ = |e|3/12π2. (i.e. β should be replaced by |e| in the printed version.) (07/06/15)
• Page 316, eqn 35.11: d4p should be ddp.
• Page 328: Using our conventions the helicity of an antiparticle should be negative that of the corresponding particle. The description is therefore for a negative helicity antiparticle. (Rather than a positive helicity particle, as stated.) (30/12/15)
• Page 329: Caption to Fig. 36.1: (c) should read h=+1; (d) should read h=-1. (30/12/15)
• Page 329, eqn 36.33: the left-most term should be followed by a ξ. (17/01/16)
• Page 342, eqn 38.10: the superscripts of us(p) and vs(p) should be r; the subscripts of asp and bsp should be rp. (30/12/15)
• Page 350: Example 39.2, paragraph 2, line 4: Using our conventions, the positron is right handed, with h=-1. The subscript labels on the particles at the end of eqn 39.14 should be modified to reflect the fact they label helicity rather than chirality. This can be done by replacing subscript R with h=1 and subscript L with h=-1. (17/01/16)
• Page 357, eqns 40.10 and 40.11: Z should read Z2. (23/12/15)
• Page 473, eqn B3: |z2| should read |z|2. (07/04/15)

#### Corrections to the reprinted edition (August 2014)

These errors occur in both the first printings and the first corrected reprint. They are corrected in the second corrected reprint, which can be identified by the note dated March 2015 that has been added to the Preface.

• Page 5, sidenote 9, first line: '|x|' should be '|x|2'. The point being that since |x|2 can be negative, we don't insist on taking a square root. (09/01/15)
• Page 13, line before eqn 1.13: the definition of g' should read g'=dg/df (rather than g'=dg/dx). (14/01/15)
• Page 14, equation 1.21: 'V' on the right hand side should not have a bar on top. (05/01/15)
• Page 45, eqn 4.58: The summation sign should come before the exponential. (29/03/15)
• Page 47, equation 4.68: the matrix in the text doesn't take into account the minus signs picked up when electrons are exchanged. The ground state energy still comes out the same whether these are considered or not, but for consistency with Chapter 3, the Hamiltonian matrix corrected for this effect should read: H = {{U, -t, t, 0}, {-t, 0, 0, -t}, {t, 0, 0, t}, {0, -t, t, U}}, where each { , , , } corresponds to a row. The ground state wavefunction for this matrix is almost the same as that given on line 2 of page 48, the only difference being that there is a minus sign in front of the third term on the right hand side. (18/02/15)
• Page 53, caption to Fig. 5.2: the inequality in the bracket should be '>' (rather than '<'). (03/11/14)
• Page 60, three lines from the bottom: the expression should read E = ±(p2+m2)1/2 (i.e. the superscript 1/2 is currently missing). (18/08/14)
• Page 94, grey box in margin, line III: Replace Wμ with ∂μWμ. (18/03/15)
• Page 96, eq (10.37): the integrand should be (J0)λρ. (03/02/15)
• Page 101, eq (11.14) should be replaced with
(10/03/15)
• Page 103, Example 11.3, eq (11.29), 2nd line: the exponent after aa should be +i(Ep-Eq)t rather than -i(Ep-Eq)t; 3rd line: the exponent after aa should be +i(Ep+Eq)t rather than -i(Ep+Eq)t. (30/09/14)
• Page 113, eqn 12.22: the coefficient '-im' should be '+im'.The final term in the example -2Ψ0Ψ should have a plus sign and the corresponding term in sidenote 8 should have a minus sign. (29/03/15)
• Page 114 eqn 12.29: Swap i to -i in the exponent (i.e. the signs should be reversed). For consistency make this change to the expression for the potential two lines below and the Fourier transform below eqn 12.30. (29/03/15)
• Page 128, example 14.3 line 1: on the right hand side, the final term is missing a factor eiα. (03/02/15)
• Page 128, example 14.3 line 2: on the right hand side, the second and fourth terms are missing a factor eiα. (25/01/15)
• Page 133, text below example 14.8, line 7: change ελ=L(q) to ε*λ=L(q). (29/03/15)
• Page 160, Fig. 17.4: the arrows in parts (b) and (c) are inconsistent. In both, the antiparticle is meant to travel from x to y. (11/02/15)
• Page 161, line 5: the phrase '... which at later time y0 collides with particle B at y ...' should read '... collides with particle A at y'. (13/08/14)
• Page 161, text before eqn (17.29): the phrase "... describing a particle propagating from spacetime point x to spacetime point y, ..." should read 'from spacetime point y to spacetime point x'. (13/08/14)
• Page 178, 2nd line of eqn (19.10): the '4' in the denominator should be '4!'. (26/08/14)
• Page 178, sidenote 3, line 3: 'ap' should be 'ap'. (14/01/15)
• Page 178, eqn (19.13): The amplitude is missing a factor of (2π)3 (2Eq)1/2 (2Ep)1/2. (26/08/14)
• Page 179, eqn (19.15): the integral representing the propagator should be multiplied by a factor of i. This extra factor should also be carried though to the next equation. (16/02/15)
• Page 183 eqn 19.18: in the first line, replace the argument z with w. (07/06/15)
• Page 229, line three: Using our conventions, the rotation is through +π/2 (rather than -π/2 as stated). (26/09/14)
• Page 262, line 8: delete 'm=' from the formula at the end of the line (the point being that m is the mass of particles for λ=0 and not for the broken excitations about the broken symmetry ground state. (04/03/15)
• Page 278, sidenote 7: the numerator in the scalar field propagator should be i (rather than 1). (05/01/15)
• Page 304, first margin note: The superscript '-1' should be removed from '[Mass]-1'. (08/01/15)
• Page 317, example 35.3: Ωd=4=1/8π2 (and not 1/8π as stated). (26/09/14)
• Page 318, There is a typo in the value of the fixed point, which occurs three times on this page. It should read 16π2ε/3 (rather than 16πε/3). This occurs in the caption to Fig. 35.3, in sidenote 11, and three lines before the end of example 35.4. (11/01/15)
• Page 345, Feynman rule 5 for vs(p) should read "for an outgoing antifermion" (rather than 'outgoing fermion'). (05/01/15)

#### Corrections to the first printings (April/June 2014)

These errors occur in the first edition, impressions 1 and 2, but are corrected in subsequent reprintings.

• page 6, eqn 21: the indices on the left-most Kronecker delta should be swapped to read δij ; those on the delta in the next part of the expression should be swapped to read δkl. [The deltas are, of course, diagonal, but this change makes the indices consistent with eqn (20).]
• page 13, eqn 1.17: the final integral on the right-hand side of this equation is missing a factor dy.
• page 24, eqn 2.37: nr in the ket (on the left-hand side of the top expression) should be replaced with nk.
• page 24, eqn 2.44: nk in the denominator should be replaced with nk!
• page 25, eqn 2.52: the summation indices should be 'k q' instead of 'p q'.
• page 26, eqn 2.61: xk should read x-k; pk should read p-k.
• page 26, five lines from the bottom: '(eqn. 2.44)' should read '(eqn. 2.41)'.
• page 41, eqn 4.29: the j's inthis equation should be k's.
• page 43, eqn 4.46: the final term in the exponential '-iq·rτ' should be replaced with '+ik·rτ'.
• page 44, line after eqn 4.51: the matrix element should read <αβ|Â|γδ>.
• page 68, two lines before eqn 7.18: 'eqn 7.16' should read 'eqn 7.17'.
• page 84, eqn 9.32: the top-left entry of the matrix should be '1' rather than '0'.
• page 106, eqn 11.41, line 2: is missing an overall minus sign.
• page 106, eqn 11.41, line 3: the overall minus sign is missing from above, a factor of -1 is also missing in the exponent.
• page 106, eqn 11.42: the expression in the bracket should read 1/x+1/(L-x).
• page 111, eqn 12.12: the right-hand side is missing an integral d3x.
• page 113, sidenote 7, line 3: the factor of g should be a λ.
• page 178, 3rd line of 2nd paragraph of 'Step IV': the x on the left-hand side of the equation should be z.
• page 193, line after eqn 20.21: ECM should not be squared.
• page 241, 6th line after eqn 26.9: 'Fig. 15.4(c)' should read 'Fig. 26.6(c)'.
• page 251, eqn 27.30: the first equation should have a minus sign on the right-hand side. The second should not.
• page 261, example 29.1, paragraph 2, line 5: the integrand should be 'A+\nabla \chi', rather than '\nabla \chi'.
• page 264, eqn 29.6: the factor nu in the denominator should be a v.
• page 277, table above section 31.3: the both instances of φ should be φ.
• page 316, eqn 35.11: the first φ in the exponent should read φ(-p) rather than φ(p).
• page 336, sidenote 2: 'tan' should read 'tanh'.
• page 351, eqn 39.11: the vertical vector on the left-hand side should be (0 0 1 0).
• page 356, two lines above 40.6: Γ' in the matrix element should be γ0.
• page 358, eqn 40.15: the factor e2 should read e4.
• page 362, final line: the denominator should have an exponent 1/2 (i.e. we take the square root of this quantity).
• page 364, eqn 41.24: the factor m in the numerator of the argument should be m2.
• page 368, chapter summary, first bullet point: the denominator should read {1 - [Π(q)-Π(0)]}1/2.
• page 395, eqn 43.60, line 1: the factor d4q should be d4p.
• page 413, line after eqn 45.10: the exponent should be q rather than p.
• page 418, note 24: the index on the final A in the expression for B should be 1, rather than 2.
• page 421, example 45.6, line 3: in keeping with the convention used in this chapter, we should take l=+1 for quasielectrons and l=-1 for quasiholes.
• page 428, the two lines before eqn 46.24: both instances of Φ, should read Ψ.
• page 438, two lines above eqn 47.22: v should be v2.
• page 452, eqn 49.8, the right-hand side is missing a factor of -1.
• page 473, eqn B.1: the numerator on the right-hand side should read 'f(z + Δz) – f(z)' rather than 'Δf(z + Δz) –f(z)'.
• page 473, eqn B.2, line 2: the second term in the numerator is missing a factor Δz.
• page 476, eqn B.19, a factor 1/2π is missing on the right-hand side.
• page 477, section B5, first line: 'The function...' should be replaced by 'The inverse of the function...'.
• page 479 eqn B.27: the denominator should read x-2 (two instances). The 'ln10' on the right hand side should read 'ln8'. As a result I1+I2 should equal 'ln4' in the next line and in eqn B.28.

With grateful thanks to Ray Artz, Petra Axolotl, Toby Baldwin, Stafford Baines, Chet Balestra, Kamil Bradler, Christoph Bruder, Jean Pierre Brunel, Yu-Ching Chen, Zu-Cheng Chen, Anatoliy Dovbnya, David Drysdale, Ernie Eld, Benjamin Frigan, Alexandros Gezerlis, Christian Gütschow, Wei-Han Hsiao, Martin Hohenadler, Patrik Iannotti, Ioannis Karafyllidis, Bernard Leikind, Li Junkang, Árpád Lukács, Perry Ma, James Manton, David Morel, Robin Oliver-Jones, Steve Palzewicz, João Penedo, Randy Roberts, Lewis Robinson, Peter Rottengatter, Marius Schaper, Franz Schindler, Sebastian Schwerdhoefer, Jimmy Snyder, Andrew Solomon, Benjamin Strekha, Sean J Swarbrick, Thomas Veness, Ming-Tso Wei, Charles Weiner and Albert Zhou.

Last updated (04/12/17)