Noncommutative Sp(2,R) gauge theories: A field theory approach to two-time physics

Journal Article · Wed Aug 15 04:00:00 EDT 2001 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.64.046005· OSTI ID:40230606

Bars, Itzhak; Rey, Soo-Jong

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, Journal Name: Physical Review D Journal Issue: 4 Vol. 64; ISSN 0556-2821
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
CAUSALITY
DIMENSIONS
FIELD EQUATIONS
FIELD THEORIES
PHASE SPACE
PHYSICS
SYMMETRY
SYMMETRY GROUPS
UNITARITY