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

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          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.

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          Author and article information

          Journal
          2015-07-29
          2015-12-10
          Article
          1507.08039
          b2e34c4b-0b60-415c-bec7-203d9b2b222b

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          08A35 (Primary), 20G20, 83E99 (Secondary)
          12 pages, contribution to Proceedings of Gribov-85 Memorial Workshop (2015)
          math-ph hep-th math.MP

          Mathematical physics,High energy & Particle physics,Mathematical & Computational physics

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