Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential

Abstract

Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position space. In both settings, we find a new type of divergence in planar graphs. It is present at and above the self-dual point. This new kind of divergence might make the construction of a Minkowski space version of the Grosse-Wulkenhaar model impossible.

26 pages, published version

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Cited by in corpus (6)

• Moyal multiplier algebras of the test function spaces of type S
• Constructive Renormalization for ${\Phi }_2^4$ Theory with Loop Vertex Expansion
• Quantum field theory in static external potentials and Hadamard states
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence
• Ultraviolet-infrared mixing on the noncommutative Minkowski space in the Yang-Feldman formalism