# Problem, exercise, anomalous magnetic moment interaction

I need to solve an exercise on Quantum Field Theory that reads as follows:

Supousse that the electron has an anomalous magnetic moment, wich makes the QED Lagrangian
(density) to have an additional term:

$$L'_I(x) = \frac{2ie}{m} \bar{\psi}(x) \sigma^{\alpha\beta} \psi(x) F_{\alpha\beta}(x)$$

where:

$$F_{\alpha\beta} = \partial_{\alpha}A_{\beta}(x) - \partial_{\beta}A_{\alpha}(x)$$

1. Find the matrix element (Feynman amplitude) for Moller's dispersion, having in account this additional
term.

*****************

I found that

$$\partial_{\alpha}\beta = \sum_k (\mp i k_{\alpha}) A^{\pm}_{\beta}(x)$$

from where, I found that:

$$2i\sigma^{\alpha\beta}F_{\alpha\beta}(x) = -i2[\check{K},\check{A}^+ - \check{A}^-]$$

where:

$$\check{K},\check{A}^+,\check{A}^-$$

denotes slash operators !!!! (I couldn't find how to draw slash operators here). The problem that I have
as from here is, that I don't know how to calculate Time Contractions to the operator:

$$A^+ - A^-$$

for example, I don't know how to calculate the Feynman propagator to the Time Contraction:

$$T\{ A(x)[A^+(y) - A^-(y)] \} = T\{ [A^+(x) + A^-(x) ][A^+(y) - A^-(y)] \}$$

Does any one knows how to proceed in this case??

best regards

Rayo