English

A natural extension of the conformal Lorentz group in a field theory context

Mathematical Physics 2016-10-24 v2 High Energy Physics - Theory math.MP

Abstract

In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field theory at fixed momentum for a spin 1/2 particle along with its antiparticle. It is shown that the essential part of the corresponding automorphism group can naturally be related to the conformal Lorentz group. In addition, the non-semisimple part of the automorphism group can be understood as "dressing" of the pure one-particle states. The studied mathematical structure may help in constructing quantum field theories in a non-perturbative manner. In addition, it provides a simple example of circumventing Coleman-Mandula theorem using non-semisimple groups, without SUSY.

Keywords

Cite

@article{arxiv.1507.08039,
  title  = {A natural extension of the conformal Lorentz group in a field theory context},
  author = {Andras Laszlo},
  journal= {arXiv preprint arXiv:1507.08039},
  year   = {2016}
}

Comments

12 pages, contribution to Proceedings of Gribov-85 Memorial Workshop (2015)