Quantum motion equation and Poincare translation invariance of noncommutative field theory

2006/01/08 by Ma, Zheng Ze
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.hep-th/0601042

Abstract

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative ϕ^⋆4 scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative ϕ^⋆4 scalar field theory for the case θ⁰ⁱ=0 of spacetime noncommutativity. Then we demonstrate the Poincar' e translation invariance for noncommutative ϕ^⋆4 scalar field theory for the case θ⁰ⁱ=0 of spacetime noncommutativity.

Related

• Commutators and propagators of Moyal star-products and microcausality for free scalar field on noncommutative spacetime
• Quantum Theory, Noncommutativity and Heuristics
• Microcausality violation of scalar field on noncommutative spacetime with the time-space noncommutativity
• Non-commutative Field Theory, Translational Invariant Products and Ultraviolet/Infrared Mixing
• Noncommutative Field Theory on Yang's Space-Time Algebra, Covariant Moyal Star Product and Matrix Model