Interacting two-time physics field theory with a BRST gauge invariant action

Abstract

We construct a field theoretic version of 2T physics including interactions in an action formalism. The approach is a Becchi-Rouet-Stora-Tyutin (BRST) formulation based on the underlying $\mathrm{Sp}(2,R)$ gauge symmetry and shares some similarities with the approach used to construct string field theory. In our first case of spinless particles, the interaction is uniquely determined by the BRST gauge symmetry, and it is different than the Chern-Simons type theory used in open string field theory. After constructing a BRST gauge invariant action for 2T physics field theory with interactions in $d+2$ dimensions, we study its relation to standard 1T physics field theory in $(d\ensuremath{-}1)+1$ dimensions by choosing gauges. In one gauge we show that we obtain the Klein-Gordon field theory in $(d\ensuremath{-}1)+1$ dimensions with unique $\mathrm{SO}(d,2)$ conformal invariant self interactions at the classical field level. This $\mathrm{SO}(d,2)$ is the natural linear Lorentz symmetry of the 2T field theory in $d+2$ dimensions. As indicated in Fig. 1, in other gauges we expect to derive a variety of $\mathrm{SO}(d,2)$ invariant 1T physics field theories as gauge fixed forms of the same 2T field theory, thus obtaining a unification of 1T dynamics in a field theoretic setting, including interactions. The BRST gauge transformation should play the role of duality transformations among the 1T physics holographic images of the same parent 2T field theory. The availability of a field theory action opens the way for studying 2T physics with interactions at the quantum level through the path integral approach.