### 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.

Original language | English |
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Article number | 1645041 |

Journal | International Journal of Modern Physics A |

Volume | 31 |

Issue number | 28-29 |

DOIs | |

Publication status | Published - Oct 20 2016 |

### Keywords

- Algebra automorphism
- Levi decomposition
- conformal Lorentz group extension
- quantum field theory

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics