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Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields

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arxiv 1809.05535 v2 pith:QAHBCEHH submitted 2018-09-14 hep-th gr-qchep-phmath.DG

classification hep-thgr-qchep-phmath.DG
keywords riemann-finslerfieldlorentz-violatingtheoriescorrespondencedimensioneffectivegeometries
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The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results provide support for open conjectures about Riemann-Finsler geometries associated with Lorentz-violating field theories.

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