Noncommutative Sp(2,R) gauge theories: A field theory approach to two-time physics
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 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.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40230606
- Journal Information:
- Physical Review D, Vol. 64, Issue 4; Other Information: DOI: 10.1103/PhysRevD.64.046005; Othernumber: PRVDAQ000064000004046005000001; 081116PRD; PBD: 15 Aug 2001; ISSN 0556-2821
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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