Duality covariant quantum field theory on noncommutative Minkowski space

Abstract

We prove that a scalar quantum field theory defined on noncommutative Minkowski spacetime with noncommuting momentum coordinates is covariant with respect to the UV/IR duality which exchanges coordinates and momenta. The proof is based on suitable resonance expansions of charged noncommutative scalar fields in a background electric field, which yields an effective description of the field theory in terms of a coupled complex two-matrix model. The two independent matrix degrees of freedom ensure unitarity and manifest CT-invariance of the field theory. The formalism describes an analytic continuation of the renormalizable Grosse-Wulkenhaar models to Minkowski signature.

32 pages; v2: Typos corrected; v3: Further typos corrected - Final version to appear in JHEP

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Cited by in corpus (13)

• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Moyal multiplier algebras of the test function spaces of type S
• Gauge Theories on Deformed Spaces
• Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential
• UV/IR duality in noncommutative quantum field theory
• Translation-Invariant Noncommutative Renormalization
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing
• Degenerate noncommutativity
• Quantization of a gauge theory on a curved noncommutative space
• Reconstruction in quantum field theory with a fundamental length