2018/06/18 by Marija Dimitrijevic Ciric, Marija Dimitrijević Ćirić, Nikola Konjik +4
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Commutative property #Field (mathematics) #Geometry #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum differential calculus #Space (punctuation) #Star (game theory) #Star product #Twist #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1103/physrevd.98.085011
published as Phys. Rev. D 98, 085011 (2018) · 23 pages 1 figure
arxiv created 2018/06/18 · openalex publication_date 2018/10/12 · arxiv updated 2018/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a noncommutative field theory in three space-time dimensions, with space-time star commutators reproducing a solvable Lie algebra. The \ensuremath⋆-product can be derived from a twist operator and it is shown to be invariant under twisted Poincar'e transformations. In momentum space the noncommutativity manifests itself as a noncommutative \ensuremath⋆-deformed sum for the momenta, which allows for an equivalent definition of the \ensuremath⋆-product in terms of twisted convolution of plane waves. As an application, we analyze the \ensuremathλ\ensuremathφ4 field theory at one loop and discuss its UV/IR behavior. We also analyze the kinematics of particle decay for two different situations: the first one corresponds to a splitting of space-time where only space is deformed, whereas the second one entails a nontrivial \ensuremath⋆-multiplication for the time variable, while one of the three spatial coordinates stays commutative.