Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions

TL;DR

This paper introduces a gauge theory in phase space with spin that unifies many 1-time physical systems via different embeddings in a higher-dimensional space with two times, revealing dualities and a common quantum structure.

Contribution

It presents a novel 2-time physics framework using OSp(1/2) gauge symmetry that unifies diverse 1-time systems and explores their dualities and shared quantum representations.

Findings

Unifies many 1-time systems through different gauge embeddings in higher dimensions.

Shows all systems share the same quantum Hilbert space with SO(d,2) symmetry.

Demonstrates how changing spin degrees of freedom alters the unification structure.

Abstract

We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are described by a 1-time formulation. Different systems of 1-time physics emerge by choosing gauges that embed ordinary time in d+2 dimensions in different ways. The embeddings have different topology and geometry for the choice of time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number of 1-time physical interacting systems, and establishes a kind of duality among them. One manifestation of the two times is that all of these physical systems have the same quantum Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical systems that are unified in the same representation depend on n. The models we study raise new questions about the nature of spacetime.