- #1

Muoniex

- 5

- 1

## Homework Statement

Hello there!

I have been studying path integral for fermionic fields, and I don't understand one detail.

I have to proove that:

[tex]\int d^4x\int d^4 y\, \overline{\eta (y)}S^+_F(x-y)(i\partial\!\!\!/-m)\Psi (x)=\int d^4x \, \overline{\eta (x)} \Psi (x)[/tex]

## Homework Equations

We know that the Feynman propagator and the Dirac operator verify:

[tex](i\partial\!\!\!/-m)S_F(x-y)=i \delta (x-y)[/tex]

## The Attempt at a Solution

This integral is supposed to do by parts.

It's clear that:

[tex]-\int d^4x\int d^4 y\, \overline{\eta (y)}S^+_F(x-y)m\Psi (x)=-\int d^4x\int d^4 y\, \overline{\eta (y)}mS^+_F(x-y)\Psi (x)[/tex]

But my problem is with the term:

[tex]i\int d^4x\int d^4 y\, \overline{\eta (y)}S^+_F(x-y)\partial\!\!\!/\Psi (x)[/tex]

This integral is supposed to do by parts, by I don't know how to do it. It's the first time I saw an integral by parts with operators and not just with functions...