Two-Time Physics with gravitational and gauge field backgrounds

TL;DR

This paper demonstrates that all interactions in a one-time d-dimensional universe can be unified and described within a two-time physics framework in d+2 dimensions, revealing hidden higher-dimensional symmetries.

Contribution

It generalizes two-time physics to include background fields, showing how diverse one-time models are related through gauge fixing in a higher-dimensional space.

Findings

Unified description of gravitational and gauge interactions in d+2 dimensions.

Explicit solutions show interactions as embedded in higher-dimensional space.

Reveals hidden higher spacetime symmetries in lower-dimensional physics.

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.