# Dirac Gamma matrices in the (-+++) metric

1. Sep 12, 2011

### brennan_t

Hi,

The typical representation of the Dirac gamma matrices are designed for the +--- metric. For example

/gamma^0 = [1 & 0 \\ 0 & -1] , /gamma^i = [0 & /sigma^i \\ - /sigma^i & 0]

this corresponds to the metric +---

Does anyone know a representation of the gamma matrices for -+++?

Can you refer me to a published article or text?

Thank you!

Thomas Brennan
Research Assistant Professor
West Virginia Wesleyan College.

2. Sep 12, 2011

### haushofer

Look for instance at "Tools for supersymmetry" by Van Proeyen, or "Supersymmetry and Gauge theory" by Lambert.

3. Sep 12, 2011

### Bill_K

Weinberg, vol I uses the (-+++) signature, and gives a representation of the Dirac matrices on p.216.

4. Sep 12, 2011

### brennan_t

Bill_K:

Thanks, what is the rest of the title? Steven Weinberg has written several books...

Is it the 'Quantum Theory of Fields, vol. I"

I think I answered my own question. Thanks.

Last edited: Sep 12, 2011
5. Sep 13, 2011

### Avodyne

Yes, that's the book.

Srednicki's text (downloadable from his web page) also has gamma matrices in (-+++) signature. But IIRC his conventions are not the same as Weinberg's.

6. Sep 13, 2011

### Avodyne

Yes, that's the book.

Srednicki's text (downloadable from his web page) also has gamma matrices in (-+++) signature. But IIRC his conventions are not the same as Weinberg's.

Actually I think Srednicki's gamma matrices are the same as yours. But he puts an extra minus sign on the RHS of the anticommutator:

$$\{\gamma^\mu,\gamma^\nu\}=-2\eta^{\mu\nu}$$