I guess the answer to this question actually should be pretty obvious, but I still have problems getting it right though. I wonder about the definition of the time ordered product for a pair of Dirac spinors. In all the books I've read it simply says:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]T\left\{\psi(x)\bar{\psi}(x')\right\} = \theta(t - t')\psi(x)\bar{\psi}(x') - \theta(t' - t)\bar{\psi}(x')\psi(x)[/tex]

The spinor indices are always left out. So should it beA:

[tex]T\left\{\psi_\alpha(x)\bar{\psi}_\beta(x')\right\} = \theta(t - t')\psi_\alpha(x)\bar{\psi}_\beta(x') - \theta(t' - t)\bar{\psi}_\beta(x')\psi_\alpha(x)[/tex]

orB:

[tex]T\left\{\psi_\alpha(x)\bar{\psi}_\beta(x')\right\} = \theta(t - t')\psi_\alpha(x)\bar{\psi}_\beta(x') - \theta(t' - t)\bar{\psi}_\alpha(x')\psi_\beta(x)[/tex]?

I personally think theAdefinition feels more natural, but when I use it in my derivations I get strange results. On the other hand, theBdefinition gives more reasonable results. It could simply be that I've done some mistakes in the derivations, but before I dig into those I want to know if I've got the definition right in the first place.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of time-ordered product for Dirac spinors

**Physics Forums | Science Articles, Homework Help, Discussion**