B Gamma Matrices and Spinors

Appendix B
Gamma Matrices and Spinors

Page 615, Eq (B.27): a term is missing in the first expression

$i∇a ¯ψΓ a + m ψ¯- e¯ψΓ aAa = ψ¯(i ⁄←∇- + m - e ⁄A) = 0. (B.27 )$
Page 619, Eq. (B.44): the order of superindices and subindices in the r.h.s should be reversed!

$Γ abΓ = Γ ab + 4Γ [d ηb] + 2 ηa ηb , (B.44 ) cd cd [a c] [d c]$
Page 619, Eq. (B.47): some signs in the r.h.s. should be reversed

$[ a b1⋅⋅⋅bn] n ab1⋅⋅⋅bn n a[b1 ⋅⋅⋅bn] Γ ,Γ ± = [1 ± (- 1) ]Γ + n[1 ∓ (- 1 )]η Γ . (B.47 )$
Addendum: From these equations we get the useful formula

$Γ aΓ b1⋅⋅⋅bnΓ = (- 1)n(d - 2n )Γ b1⋅⋅⋅bn . a$
Page 625, Eq. (B.93): a factor of 1∕sqrt2 is missing in the r.h.s. of the second equation

$a a -1 1√-- 1 γM = S γW S , S = I2×2 ⊗ 2(I2×2 - iσ ) , (B.93 )$
Addendum: Page 625: the duality formula for the 5-dimensional gammas takes the form

$[n∕2] ˆγˆa1⋅⋅⋅ˆan = (--1)----ˆϵˆa1⋅⋅⋅ˆanˆb1⋅⋅⋅ˆb5-nˆγˆ ˆ . (5 - n)! b1⋅⋅⋅b5- n$