  Phase-space and its relativistic extension is a natural space for realizing
Sp(2,R) symmetry through canonical transformations. On a Dx2 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 signature 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.
