Noncommutative Sp(2,R) gauge theories:: A field theory approach to two-time physics -: art. no. 046005

Phase space and its relativistic extension is a natural space for realizing Sp(2,R) symmetry through canonical transformations. On a (D X 2)-dimensional covariant phase space. we formulate noncommutative field theories, where Sp(2,R) plays a role as either a global or a gauge symmetry group. In both cases these field theories have potential applications, including certain aspects of string, theories, M theory, as well as quantum field theories. If interpreted as living in lower dimensions, these theories realize Poincare symmetry linearly in a way consistent with causality and unitarity. In case Sp(2,R) is a gauge symmetry, we show that the spacetime si-nature is determined dynamically as (D-2,2). The resulting noncommutative Sp(2,R) gauge theory is proposed as a field theoretical formulation of two-time physics: classical field dynamics contains all known results of "two-time physics." including the reduction of physical spacetime from D to (D-2) dimensions, with the associated "holography" and "duality" properties. In particular, we show that the solution space of classical noncommutative field equations put all massless scalar. gauge, gravitational. and higher-spin fields in (D-2) dimensions on equal footing, reminiscent of string excitations at zero and infinite tension limits.