### 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 |
---|---|

Article number | 1645041 |

Journal | International Journal of Modern Physics A |

Volume | 31 |

Issue number | 28-29 |

DOIs | |

Publication status | Published - Oct 20 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

**A natural extension of the conformal Lorentz group in a field theory context.** / László, A.

Research output: Contribution to journal › Article

*International Journal of Modern Physics A*, vol. 31, no. 28-29, 1645041. https://doi.org/10.1142/S0217751X1645041X

}

TY - JOUR

T1 - A natural extension of the conformal Lorentz group in a field theory context

AU - László, A.

PY - 2016/10/20

Y1 - 2016/10/20

N2 - 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.

AB - 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.

KW - Algebra automorphism

KW - conformal Lorentz group extension

KW - Levi decomposition

KW - quantum field theory

UR - http://www.scopus.com/inward/record.url?scp=84992361750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992361750&partnerID=8YFLogxK

U2 - 10.1142/S0217751X1645041X

DO - 10.1142/S0217751X1645041X

M3 - Article

AN - SCOPUS:84992361750

VL - 31

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 28-29

M1 - 1645041

ER -