- #1

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Supousse that the electron has an anomalous magnetic moment, wich makes the QED Lagrangian

(density) to have an additional term:

[tex]

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

[/tex]

where:

[tex]

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

[/tex]

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

term.

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

I found that

[tex]

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

[/tex]

from where, I found that:

[tex]

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

[/tex]

where:

[tex]

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

[/tex]

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:

[tex]

A^+ - A^-

[/tex]

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

[tex]

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

=

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

[/tex]

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

best regards

Rayo