Time ordered perturbation theory for non-local interactions; applications to NCQFT

Abstract

In the past decades, time ordered perturbation theory was very successful in describing relativistic scattering processes. It was developed for local quantum field theories. However, there are field theories which are governed by non-local interactions, for example non-commutative quantum field theory (NCQFT). Filk (Phys. Lett. B 376 (1996) 53) first studied NCQFT perturbatively obtaining the usual Feynman propagator and additional phase factors as the basic elements of perturbation theory. However, this treatment is only applicable for cases, where the deformation of space-time does not involve time. Thus, we generalize Filk's approach in two ways: First, we study non-local interactions of a very general type able to embed NCQFT. And second, we also include the case, where non-locality involves time. A few applications of the obtained formalism will also be discussed.

arXiv comment21 pages, 2 figures

References in corpus (15)

• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Towards High-Precision Predictions for the MSSM Higgs Sector
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• On the unitarity problem in space/time noncommutative theories
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Space/time noncommutative field theories and causality
• Unitarity in space-time noncommutative field theories
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory
• Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections

Cited by in corpus (16)

• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• On $\kappa$-Deformation and UV/IR Mixing
• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Quantum Spacetime: a Disambiguation
• Gauge Theories on Deformed Spaces
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Non Local Theories: New Rules for Old Diagrams
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• Perturbation theory of the space-time non-commutative real scalar field theories
• Translation-Invariant Noncommutative Renormalization
• Towards UV Finite Quantum Field Theories from Non-Local Field Operators
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Consistent Construction of Perturbation Theory on Noncommutative Spaces
• DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
• Wick rotation for quantum field theories on degenerate Moyal space(-time)