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  A new kind of local symmetry without gauge bosons

Laszlo, A., & Andersson, L. (in preparation). A new kind of local symmetry without gauge bosons.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-C48B-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-C48C-1
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1909.02208.pdf (Preprint), 307KB
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 Creators:
Laszlo, Andras, Author
Andersson, Lars1, Author              
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: In conventional gauge theories, any local gauge symmetry generator is accompanied by a corresponding gauge boson in order to compensate the transformation of the gauge-covariant derivation against the local gauge transformations as acting on the matter fields. Indeed, whenever the gauge group is purely compact, as in usual gauge theories, the invocation of corresponding gauge bosons as compensating fields is unavoidable. That is because there exist no nontrivial forgetful homomorphisms onto some smaller Lie groups from the full gauge group. In this paper we show a mechanism that at the price of allowing some non-semisimple component of the gauge group besides the compact part, it is possible to construct such Lagrangians that the non-semisimple part of the local gauge group only acts on the matter fields, without invoking corresponding gauge bosons. It shall be shown that already the ordinary Dirac equation admits such a hidden symmetry related to the dilatation group, thus this mechanism cannot be called unphysical. Then, we give our more complicated example Lagrangian, in which the gauge group is an indecomposable Lie group built up of a nilpotent part and of a compact part. Since the nilpotent part does carry also Lorentz charges in our example, the first order symmetries of the pertinent theory give rise to a unified gauge--Poincar\'e group, bypassing Coleman--Mandula and related no-go theorems in a different way in comparison to SUSY. The existence of a local symmetry without a gauge boson is already mathematically very striking, but this new mechanism might even be useful to eventually try to substitute SUSY for a unification concept of symmetries.

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 Dates: 2019-09-05
 Publication Status: Not specified
 Pages: 23 pages, 4 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1909.02208
URI: http://arxiv.org/abs/1909.02208
 Degree: -

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