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Two-Time Physics with gravitational and gauge field backgrounds

Itzhak Bars
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Abstract

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the worldline formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1) +1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target d+2 dimensional spacetime. The gravitational background obeys a null homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher d+2 dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden.

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Itzhak Bars. 2000-08-11. Two-Time Physics with gravitational and gauge field backgrounds. https://doi.org/10.1103/physrevd.62.085015

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