I. Bars et Sj. Rey, Noncommutative Sp(2,R) gauge theories: A field theory approach to two-timephysics - art. no. 046005, PHYS REV D, 6404(4), 2001, pp. 6005
Phase space and its relativistic extension is a natural space for realizing
Sp(2,R) symmetry through canonical transformations. On a (D X 2)-dimension
al 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. I
f interpreted as living in lower dimensions, these theories realize Poincar
e symmetry linearly in a way consistent with causality and unitarity. In ca
se Sp(2,R) is a gauge symmetry, we show that the spacetime si-nature is det
ermined 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, w
ith the associated "holography" and "duality" properties. In particular, we
show that the solution space of classical noncommutative field equations p
ut all massless scalar. gauge, gravitational. and higher-spin fields in (D-
2) dimensions on equal footing, reminiscent of string excitations at zero a
nd infinite tension limits.