Student Friendly Introduction to QFT · Problem 25

Spinors: Spin ½ Fields

Physics — QFT · dirac-coefficient-squares-zero

Problem

Prove that from the second of (4-83) and similar relations for

d_r(\mathbf{p})

and

d_r^\dagger(\mathbf{p})

\left(c_r(\mathbf{p})\right)^2 = 0 \qquad \left(d_r^\dagger(\mathbf{p})\right)^2 = 0 \qquad \left(d_r(\mathbf{p})\right)^2 = 0 \tag{4-85}

Note that none of (4-84) and (4-85) would be true if the coefficients obeyed commutation, rather than anti-commutation, relations.