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• W2011095046 abstract "The Maxwell algebra is a noncentral extension of the Poincar'e algebra, in which the momentum generators no longer commute, but satisfy $[{P}_{ensuremath{mu}},{P}_{ensuremath{nu}}]={Z}_{ensuremath{mu}ensuremath{nu}}$. The charges ${Z}_{ensuremath{mu}ensuremath{nu}}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar'e, this being the symmetry algebra of very special relativity. It admits an analogous noncentral extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to ${mathrm{DISim}}_{b}$, where $b$ is a nontrivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the ${mathrm{DISim}}_{b}$ algebra is isomorphic to the extended Schrodinger algebra with its standard deformation parameter $z$, when $b=frac{1}{1ensuremath{-}z}$." @default.
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• W2011095046 date "2010-09-01" @default.
• W2011095046 modified "2023-10-11" @default.
• W2011095046 title "Deforming the Maxwell-Sim algebra" @default.
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• W2011095046 doi "https://doi.org/10.1103/physrevd.82.065002" @default.
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