U*(1,1) Noncommutative Gauge Theory As The Foundation of 2T-Physics in Field Theory

TL;DR

This paper develops a noncommutative gauge theory in d+2 dimensions that unifies various gauge principles in a single framework, providing a foundation for 2T-Physics and revealing new interactions among gauge fields.

Contribution

It introduces a simple noncommutative phase space gauge theory based on u*(1,1), unifying Maxwell, Einstein, and high spin gauge principles within 2T-Physics.

Findings

Reproduces first quantized worldline theory with background fields

Constructs a gauge invariant action with nonlinear equations of motion

Outlines a matrix version with large N limit

Abstract

A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2 dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a remarkable unification of several gauge principles in d dimensions, including Maxwell, Einstein and high spin gauge principles, packaged together into one of the simplest fundamental gauge symmetries in noncommutative quantum phase space in d+2 dimensions. A gauge invariant action is constructed and its nonlinear equations of motion are analyzed. Besides elegantly reproducing the first quantized worldline theory with all background fields, the field theory prescribes unique interactions among the gauge fields. A matrix version of the theory, with a large N limit, is also outlined