Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules

Abstract

Assuming the S-matrix on noncommutative (NC) spacetime can still be developped perturbatively in terms of the time-ordered exponential of the interaction Lagrangian, we investigate the perturbation theory of NC field theory. We first work out with care some typical Green functions starting from the usual concepts of time-ordering and commutation relations for free fields. The results are found to be very different from those in the naive approach pursued in the literature. A simple framework then appears naturally which can incorporate the new features of our results and which turns out to be the usual time-ordered perturbation theory extended to the NC context. We provide the prescriptions for computing S-matrix elements and Green functions in this framework. We also emphasize that the naive seemingly covariant approach cannot be reproduced from the current one, in contrast to the field theory on ordinary spacetime. We attribute this to the phase-like nonlocal interaction intrinsic in NC field theory which modifies the analytic properties of Green functions significantly.

19 pages, 1 figure using axodraw; version 2: typos fixed and one ref updated, to appear in Eur Phys J C

References in corpus (3)

• The quantum structure of spacetime at the Planck scale and quantum fields
• On the unitarity problem in space/time noncommutative theories
• Unitarity in space-time noncommutative field theories

Cited by in corpus (62)

• General Properties of Noncommutative Field Theories
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Space/time noncommutative field theories and causality
• kappa-deformed Spacetime From Twist
• Path Integral for Space-time Noncommutative Field Theory
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• Noncommutative Field Theory from twisted Fock space
• Unitarity of Time-Like Noncommutative Gauge Theories: The Violation of Ward Identities in Time-Ordered Perturbation Theory
• $t\to bW$ in NonCommutative Standard Model
• Some properties of the integrable noncommutative sine-Gordon system
• Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
• Some Phenomenological Consequences of the Time-Ordered Perturbation Theory of QED on Noncommutative Spacetime
• Time ordered perturbation theory for non-local interactions; applications to NCQFT
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Quantum Spacetime: a Disambiguation
• Duality covariant quantum field theory on noncommutative Minkowski space
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Quantized equations of motion in non-commutative theories
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• Effects of Unparticles on Running of Gauge Couplings
• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• Unitary Quantum Field Theory on the Noncommutative Minkowski space
• Ultraviolet Finiteness of the averaged Hamiltonian on the noncommutative Minkowski space
• Infrared cutoffs and the adiabatic limit in noncommutative spacetime
• The ultraviolet infrared mixing problem on the noncommutative Moyal space
• On the unitarity of higher-dervative and nonlocal theories
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Non Local Theories: New Rules for Old Diagrams
• On the Renormalization of Non-Commutative Field Theories
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Canonical analysis of space-time noncommutative theories and gauge symmetries
• Canonical formalism and quantization of perturbative sector of higher-derivative theories
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• UV/IR duality in noncommutative quantum field theory
• Violation of Remaining Lorentz Symmetry in the Approach of Time-Ordered Perturbation Theory to Space-Time Noncommutativity
• Perturbation theory of the space-time non-commutative real scalar field theories
• Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory
• Translation-Invariant Noncommutative Renormalization
• Noncommutative geometry and fundamental interactions: the first ten years
• On Evaluation of Nonplanar Diagrams in Noncommutative Field Theory
• Noncommutative Time in Quantum Field Theory
• Perturbative quantization of two-dimensional space-time noncommutative QED
• Towards UV Finite Quantum Field Theories from Non-Local Field Operators
• Emergence of Time from Dimensional Reduction in Noncommutative Geometry
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Dynamical generation of mass in the noncommutative supersymmetric Schwinger model
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Consistent Construction of Perturbation Theory on Noncommutative Spaces
• Higher Derivative Operators in the Noncommutative Schwinger Model
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Quantized Equations of Motion and Currents in Noncommutative Theories
• DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
• Retarded Functions in Noncommutative Theories
• The interface of noncommutative geometry and physics
• Comment on the Decoupling of UV and IR Divergencies within Dimensional Regularization in Noncommutative Theories
• Comments on Noncommutative Field Theories
• Wick rotation for quantum field theories on degenerate Moyal space(-time)
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space
• Quantum Space-Time and Noncommutative Gauge Field Theories