Perturbation theory of the space-time non-commutative real scalar field theories

Abstract

The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian formalism of the second quantized operators, with the emphasis of the so-called minimal realization of the time-ordering step function and of the importance of the $\star$-time ordering. The Feynman rule is established and is presented using ${\varphi }^4$ scalar field theory. It is shown that the divergence structure of space-time non-commutative theory is the same as the one of space-space non-commutative theory, while there is no UV-IR mixing problem in this space-time non-commutative theory.

arXiv commentLatex 26 pages, notations modified, add references

References in corpus (16)

• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Space-Time Noncommutative Field Theories And Unitarity
• Space/Time Non-Commutativity and Causality
• On the unitarity problem in space/time noncommutative theories
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Hamiltonian Formalism for Space-time Non-commutative Theories
• Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
• Noncommutative Gauge Theory without Lorentz Violation
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
• Unitarity in space-time noncommutative field theories
• Unitarity of Time-Like Noncommutative Gauge Theories: The Violation of Ward Identities in Time-Ordered Perturbation Theory
• Time ordered perturbation theory for non-local interactions; applications to NCQFT
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory

Cited by in corpus (7)

• Path Integral for Space-time Noncommutative Field Theory
• Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory
• Galilean symmetry in noncommutative Gravitational Quantum Well
• Blackbody radiation in κ-Minkowski spacetime
• On the unitarity of higher-dervative and nonlocal theories
• Canonical formalism and quantization of perturbative sector of higher-derivative theories
• Causality in Non-Commutative Quantum Field Theories