- #1

mdb71

- 5

- 3

We want to get from the LHS to the RHS of the following expression

$$\bar{u}(p')[-\frac{1}{2}l^2\gamma^\mu + (z\not{p}-y\not{q})\gamma^{\mu}(z\not{p}+(1-y)\not{q}) + m^2\gamma^{\mu}-2m((1-2y)q^{\mu}+2zp^{\mu})]u(p)$$ $$ = \bar{u}(p')[\gamma^{\mu}(-\frac{1}{2}l^2+(1-x)(1-y)q^2+(1-2z-z^2)m^2)+(p'^{\mu}+p^{\mu})mz(1-z)+q^{\mu}m(z-2)(x-y)]u(p)$$

using

$$ q \equiv p'-p, \not{p}u(p) = mu(p), \bar{u}(p')\not{p'} = m\bar{u}(p'), \bar{u}(p')\not{q}u(p) = 0,\\

x+y+z = 1$$

Thanks a lot in advance!