Possible alternative mechanism to SUSY: Conservative extensions of the Poincaré group

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A group theoretical mechanism is outlined, which can indecomposable extend the Poincaré group by the compact internal (gauge) symmetries at the price of allowing some nilpotent (or, more precisely: solvable) internal symmetries in addition. Due to the presence of this nilpotent part, the prohibitive argument of the well known Coleman-Mandula, McGlinn no-go theorems do not go through. In contrast to SUSY or extended SUSY, in our construction the symmetries extending the Poincaré group will be all internal, i.e. they do not act on the spacetime, merely on some internal degrees of freedom — hence the name: conservative extensions of the Poincaré group. Using the Levi decomposition and O’Raifeartaigh theorem, the general structure of all possible conservative extensions of the Poincaré group is outlined, and a concrete example group is presented with U(1) being the compact gauge group component. It is argued that such nilpotent internal symmetries may be inapparent symmetries of some more fundamental field variables, and therefore do not carry an ab initio contradiction with the present experimental understanding in particle physics. The construction is compared to (extended) SUSY, since SUSY is somewhat analogous to the proposed mechanism. It is pointed out, however, that the proposed mechanism is less irregular in comparison to SUSY, in certain aspects. The only exoticity needed in comparison to a traditional gauge theory setting is that the full group of internal symmetries is not purely compact, but is a semi-direct product of a nilpotent and of a compact part.

Original languageEnglish
Title of host publicationQuantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017
EditorsVladimir Dobrev
PublisherSpringer New York LLC
Pages353-362
Number of pages10
Volume255
ISBN (Print)9789811321788
DOIs
Publication statusPublished - Jan 1 2018
EventInternational Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017 - Varna, Bulgaria
Duration: Jun 19 2017Jun 25 2017

Other

OtherInternational Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017
CountryBulgaria
CityVarna
Period6/19/176/25/17

Keywords

  • Gauge group
  • GUT
  • Levi decomposition theorem
  • O’Raifeartaigh theorem
  • Poincaré group
  • Unification

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    László, A. (2018). Possible alternative mechanism to SUSY: Conservative extensions of the Poincaré group. In V. Dobrev (Ed.), Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017 (Vol. 255, pp. 353-362). Springer New York LLC. https://doi.org/10.1007/978-981-13-2179-5_27