Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to deduce the suspersymmetry transformation of the chiral multiplet out of the superfield formalism. In doing this I got stuck with this:

[tex]\theta^{\alpha}\sigma^{\mu}_{\alpha\dot{\alpha}}\overline{\sigma}^{\dot{\alpha}\beta}_{\nu}\theta_\beta(\partial_\mu\psi_\gamma\sigma^{\nu}_{\gamma\dot{\gamma}}\overline{\xi}^{\dot{\gamma}})[/tex]

Here I wrote all the indices explicitly, with the undotted and dotted respectively left and right handed 2D Weyl indices (theta's anti commuting).

What bothers me is the part in front of the paragraphs, I would like to get something like this:

[tex]\theta^{\alpha}\epsilon_{\alpha\beta}\theta^\beta(\partial_\mu\psi_\gamma\sigma^{\mu}_{\gamma\dot{\gamma}}\overline{\xi}^{\dot{\gamma}})[/tex]

Notice that there is the contraction now in the paragraph on space time indices. I think it's not that difficult, one has to use the clifford algebra commutation relation I guess, but I don't see it coming out. Maybe tracing over it would also work. Any help would be appreciated much.

greetz

hendrik

**Physics Forums - The Fusion of Science and Community**

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!

# Calculation trafo chiral multiplet

Loading...

Similar Threads - Calculation trafo chiral | Date |
---|---|

A NLO and NNLO order calculation for HardQCD in PYthia8.2 | Mar 15, 2018 |

I Calculation Of the energy Of beta decay in tritium | Dec 7, 2017 |

A How to calculate the energy of Gamma rays in fusion | Nov 10, 2017 |

I Calculating conditions necessary for nuclear fusion | Oct 25, 2017 |

I Helicity and chirality | Jul 10, 2017 |

**Physics Forums - The Fusion of Science and Community**