2009/08/31 by Dorothea Bahns · 14 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Euclidean geometry #Field (mathematics) #Field theory (psychology) #Geometry #Mathematical physics #Mathematics #Minkowski space #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum #Quantum differential calculus #Quantum field theory #Quantum gravity #Quantum mechanics #Renormalization #Scalar field #Scalar field theory #Theoretical physics #hep-th #math-ph #math.MP #msc:46F20 #msc:81T75
paper · pdf · doi:10.1007/s00023-010-0061-4
published in Annales Henri Poincaré 11(7), 1273-1283 (Birkhäuser)
arxiv created 2009/08/31 · openalex publication_date 2010/12/01 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.