Noncommutativity and theta-locality

Abstract

In this paper, we introduce the condition of theta-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutator of observables behaves at large spacelike separation like $\exp (-|x-y{|}^2/\theta )$, where $\theta$ is the noncommutativity parameter. The rigorous formulation given in the paper implies averaging fields with suitable test functions. We define a test function space which most closely corresponds to the Moyal star product and prove that this space is a topological algebra under the star product. As an example, we consider the simplest normal ordered monomial $:\varphi \star \varphi :$ and show that it obeys the theta-locality condition.

LaTeX, 17 pages, no figures; minor changes to agree with published version

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Cited by in corpus (14)

• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
• Higher Spin Fields in Siegel Space, Currents and Theta Functions
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Moyal multiplier algebras of the test function spaces of type S
• Duality covariant quantum field theory on noncommutative Minkowski space
• Particle phenomenology on noncommutative spacetime
• Algebras with convergent star products and their representations in Hilbert spaces
• Twisted convolution and Moyal star product of generalized functions
• Noncommutative deformations of quantum field theories, locality, and causality
• Failure of microcausality in noncommutative field theories
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Integral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators
• Reconstruction in quantum field theory with a fundamental length
• Microcausality of spin-induced noncommutative theories