Quantized equations of motion in non-commutative theories

Abstract

Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents can not be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries SO(1,1) x SO(2) and translation invariance turn out to be respected. Unitarity is guaranteed as well.

22 pages, uses axodraw.sty. Published version

References in corpus (2)

• Violation of Remaining Lorentz Symmetry in the Approach of Time-Ordered Perturbation Theory to Space-Time Noncommutativity
• Quantization of Space-time Noncommutative Theory

Cited by in corpus (7)

• Remarks on twisted noncommutative quantum field theory
• On the Renormalization of Non-Commutative Field Theories
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• Translation-Invariant Noncommutative Renormalization
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Conjugate variables in quantum field theory and a refinement of Paulis theorem
• Retarded Functions in Noncommutative Theories