Student Friendly Introduction to QFT · Problem 30

Vectors: Spin 1 Fields

Physics — QFT · gamma-matrix-anticommutation

Problem

Prove i) several of the anti-commutation relations (4-157) by plugging and chugging for different values of μ\mu and ν\nu, and/or ii) all of the anti-commutation relations (4-157) using (4-6). (Hint for part ii): For i≠ji \neq j, use the top line of (4-6), insert ββ=I\beta\beta = I in between the factors in each term, and take αiβ=−βαi\alpha_i\beta = -\beta\alpha_i. For ii and 00, pre-multiply [αi,β]+=0[\alpha_i, \beta]_+ = 0 by β\beta and substitute γμ\gamma^\mu values. For i=ji = j, insert ββ\beta\beta between the factors and use [αi,β]+[\alpha_i, \beta]_+. For 00 and 00, it is simple.)

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