Dualities among 1T-Field Theories with Spin, Emerging from a Unifying 2T-Field Theory

TL;DR

This paper explores how 2T-physics in d+2 dimensions relates to 1T-physics through dualities and hidden symmetries, providing a unifying framework that connects various 1T field theories across different spacetime backgrounds.

Contribution

It develops a quantitative framework linking 2T and 1T field theories, revealing dualities and hidden symmetries among 1T theories in diverse gravitational backgrounds.

Findings

Identifies dualities among 1T field theories in various spacetimes.

Constructs generators of hidden SO(d,2) symmetry in conformally flat backgrounds.

Provides evidence for the underlying 2T-physics structure and higher-dimensional spacetime.

Abstract

The relation between two time physics (2T-physics) and the ordinary one time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the Standard Model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS(d-k) x S(k) and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.