Corrections Field Theory Course

All corrections have been implemented in the files that can be downloaded.

The first part of the list collects the accumulated corrections since the (printed) version of September 1998 till December 2000. I thank the students of the Fall-2000 course for contributing to these corrections.

For those that downloaded the files from 2001 onwards (the first page will state "Corrected version, January 2001"), later corrections (with special thanks to Robert-Jan Kooman, Fall 2004 course and Jörn Venderbos, Spring 2007 course) will be collected in a separate part.

Corrections till December 2000, Fall 1998 version

Pg. 3, eq. (1.4), take d/dt of the left hand side.
Pg. 4, eq. (1.7), last line: replace sinh(u+v) by sinh(u).
Pg. 4-5, between eq. (2.3) and (2.9), quite some factors of hbar (not put to one in this section) were missing.
Pg. 14, eq. (4.15), last index should be n-2, not n-1.
Pg. 16, eq. (4.19), the argument (x) should be (k).
Pg. 17, eq. (4.25), the argument (x) should be (k).
Pg. 18, eq. (5.8), 2nd and 4th line, under the integral (t) should be (t₁).
Pg. 23, eq. (6.24), (b_i) should be (b_l).
Pg. 23, eq. (6.27), multiply right hand side with -1/2.
Pg. 24-26, F as defined in eq. (6.33), is the free energy up to a constant (step size divided by hbar).
Pg. 25, eq. (6.39), some small typos corrected.
Pg. 25, eq. (6.42), some sign mistakes corrected.
Pg. 27, eq. (6.58), delta function in ij added.
Pg. 27, eq. (6.59), m in potential term missing.
Pg. 29, eq. (7.6), drop the minus sign on the left hand side.
Pg. 29, eq. (7.8), interchange the integration boundaries t₂ and t₁ in the exponent.
Pg. 29, just above eq. (7.10), replace <0|...> by <...|0>.
Pg. 31, eq. (7.20), the first field insertion should be at t₂ instead of t₁.
Pg. 32, eq. (7.25), drop epsilon-bar, it was put to 1 in this section.
Pg. 32, just above eq. (7.26), the left hand side should read a(p)+a⁺(-p), noting that <0|a⁺(-p)=0.
Pg. 34, eq. (8.2), replace V by -V.
Pg. 39, below eq. (9.9), discussion added to clarify that usually tadpole diagrams (with one external line) are assumed to be removed (by a shift in the field).
Pg. 40, eq. (9.17), multiply the right hand side with exp(G_J=0).
Pg. 43, eq. (9.26), 2nd line, for the last delta function, the index on k-vector has to be 1, instead of 2.
Pg. 45, eq. (11.4), divide right hand side by 2.
Pg. 46, eq. (11.8), first line, divide right hand side by 2.
Pg. 49, eq. (12.18), add "=0".
Pg. 49, last line, replace L by K.
Pg. 50, 2nd line from bottom, restore balance in index (last gamma matrix should have index nu, instead of mu)
Pg. 68, eq. (15.66), for the middle two identities the index b should hang on the closing bracket.
Pg. 76, eq. (17.19), not wrong, but changing sign of m (4 times) is what was intended.
Pg. 78, eq. (17.27), multiply the right hand side with sign(k₀). This way the result also holds for anti-particles, with momentum flowing along the arrow (so k₀ < 0). The overall minus sign follows from eq. (13.18).
Pg. 82, eq. (17.50), replace cos by cos².
Pg. 92, eq. (20.16), replace M_ab by qM_ab.
Pg. 92, table 7 replace M^-1 by (qM)^-1.
Pg. 93, eq. (20.18), replace M^ab by qM^ab.
Pg. 95, immediately above eq. (21.10), interchange the definitions of W⁺ and W^-.
Pg. 97, eq. (21.26), the SU(3) generators usually have an extra minus sign. The ones listed now are related to the Gell-Mann matrices by a factor -i/2.
Pg. 102, eq. (22.10), replace beta(n-1,k) by B(n,k).
Pg. 104, eq. (22.23), take the square root of the Z-factor.
Pg. 107, eq. (22.37), for Z_A, pi needs to be squared.
Pg. 107, below eq. (22.37), do not redefine alpha. Meant was that alpha_B/e_B² is finite and alpha/e² remains free of renormalisations (below eq. (22.39)).
Pg. 107, eq. (22.39), replace alpha by alpha_B.
Pg. 108, eq. (22.40), replace alpha by alpha_B.
Pg. 108, eq. (22.42), invert the power of mu.
Pg. 109, below eq. (22.47), divide c by pi ².
Pg. 118, prob. 10.c.3, better Hint added.
Pg. 138, prob. 32, replace p+eA by p-eA. Please note: to respect covariance p_k=-id/dx^k, whereas in writing three vectors the conventions are with indices up. In most textbooks, however, p^k=-id/dx^k. With our metric this would introduce an extra sign.
This problem goes back to the wrong choice above eq. (12.1), see corrections in the January 2001 version.
Pg. 140, prob. 36, 4th line from the bottom, interchange the definitions of W⁺ and W^-.

Corrections in the January 2001 version

Pg. 2-4, eq. (1.1) should be numbered (1.0), but equation numbers were in this chapter increased by 1.
Pg. 5, eq.(2.7), the complex conjugate of pi must be interchanged.
Pg. 9, in eq. (3.6) a factor of g is missing in front of phi⁴/4!.
Pg. 12, just above eq. (3.27), assignement of E and B adjusted.
Pg. 14, right hand side of eq. (4.14) the two argument y should be replaced by x.
Pg. 15, line below eq. (4.17), the index i_v does NOT include x (of course). It should have read "Here the index i_v runs over all vertices and sources (so it .....".
Pg. 15, closing bracket inserted after "interaction term.".
Pg. 40, in eq. (9.17), q_r and r were interchanged in the argument of the product over r. Also needs to be corrected in the last paragraph on pg. 42 (it also better refer to eq. (9.17) at this place, rather than to eq. (9.16)).
Pg. 45, just below eq. (11.4) the first i under the square root should be removed.
Pg. 47, last of eq. (12.3), the last index k should be j.
Pg. 47-51, above eq. (12.1), the sign in the choice for the momentum operator was wrong, which changes the sign of the momenta in eqs. (12.2), (12.7), (12.10-11), (12.16), (12.18) and (12.39-40) (changing eqs. (12.7), (12.10-11) and (12.40) was implemented only for consistency in the presentation).
Pg. 55, in eq. (14.3) alpha should have the index j down to avoid confusion concerning the sign.
Pg. 56, (14.8) should end with a comma.
Pg. 71/73, in the first expression in eq. (16.9) the spatial component should have a minus sign, because the spin wave functions have their Lorentz index down! Likewize in the expression for n(k) in eq. (16.21) the spatial component should {\bf not} have a minus sign (otherwize n(k) is proportional to k and the vectors in eq. (16.21), together with k, would not form a complete set).
Pg. 76, in eq. (17.18) some sign errors in the first two terms were fixed.
Pg. 76, in eq. (17.19) an unbalanced index in the 3rd term was fixed.
Pg. 79, above eq.(17.36) "that" is replaced by "the" ("Finally we use the identity")
Pg. 80, in eq. (17.39) kappa should already be set to -1, and the last identity of eq. (17.38) was only correct for kappa=-1, but is now valid for arbitrary kappa.
Pg. 83, just above eq. (18.5) the Lie-product is of course NOT associative, instead one has to require the Jacobi identity as defined in eq. (18.12).
Pg. 84, in eq. (18.14) replace -f_abc by f_acb and in eq. (18.18) replace f_abc by f_bca (these epressions were meant to hold without making use of the cyclic symmetry).
Pg. 93, above chapter 21 it should read section 12-4-1.
Pg. 96, in eq. (21.15) the helicity assignments should be interchanged.
Pg. 97, third line below (21.26), SU(N) should be SU(N).
Pg. 98, below table 8, Cabibbo should be replaced by Cabibbo-Kobayashi-Maskawa.
Pg. 105, in eq. (22.24) the sign of the last two terms should change sign (cmp. eq. (22.19)).
Pg. 108, after (22.41), SU(N) should be SU(N), and at the end of next line it should read sect. 12-3-4.
Pg. 112, last bracket in 2d. "withe the t₀ term" should be "with the t₀ term".
Pg. 117, in (2) the last A should be a vector.
Pg. 124-125, prob. 16.c.1-2, integrations should be over d⁴x and d⁴y. In prob. 16.c.3, some delta functions were missing.
Pg. 125, prob. 17.b, a coupling constant was missing.
Pg. 130, prob. 22.b.3, first line, in the definition of Sigmaⁱ the right hand side has to be divided by two.
Pg. 136, prob. 31.a, the inner brackets in the definition of the adjoint representation is misplaced and should be omitted.
Pg. 137, prog. 32.b, T=iq should be replaced by T=i to follow the conventions in prob. 31.
Pg. 138, prob. 32, replace p-eA by p+eA due to the change in sign to p_k=id/dx^k. The footnote has been adapted. (Compare the correction above eq. (12.1) on pg. 47.)
Pg. 138, prob. 33, the way it was formulated is confusing. Replace sigma' by sigma+v in the potential term of the Lagrangian and in 33.b (2nd line below (2)). In 33.a show that the Lagrangian has a linear term in sigma and determine its coefficient. Show that the coefficient is zero if phi=0 and sigma=0 corresponds to a minimum, and check that the pions are massless and the sigma has a mass mu.
Pg. 139, prob. 34, the sign of the interaction term in the field tensor should be changed from a minus to a plus.
Pg. 141, prob. 37, 3rd line, Gev should read GeV.
Pg. 142, prob. 37.e, replace -i for the propagator in front of the decay width term by i (cmp. eq. (11.4) on pg. 45).
Pg. 144, prob. 39, F² should come with a minus sign in the Lagrangian. Related to this the sign of the 0^th order two-point function and its relation to the propagator has to be changed.
Pg. 146, below (1) the sentence should end with "in terms of g and M_W."