Schwinger functions in noncommutative quantum field theory

Abstract

It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.

References in corpus (1)

• A translation-invariant renormalizable non-commutative scalar model

Cited by in corpus (10)

• Quantum Spacetime: a Disambiguation
• Gauge Theories on Deformed Spaces
• Solvable limits of a 4D noncommutative QFT
• The ultraviolet infrared mixing problem on the noncommutative Moyal space
• Quantum field theory in static external potentials and Hadamard states
• On the Renormalization of Non-Commutative Field Theories
• Aspects of perturbative quantum field theory on non-commutative spaces
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Degenerate noncommutativity
• Wick rotation for quantum field theories on degenerate Moyal space(-time)