Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane

Abstract

Field theories on the Groenewold-Moyal(GM) plane are studied using the Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields is treated in detail. The S-matrix elements in this non-perturbative approach are shown to be equal to the interaction representation S-matrix elements. This is a new non-trivial result: in both cases, the S-operator is independent of the noncommutative deformation parameter ${\theta }_{\mu \nu }$ and the change in scattering amplitudes due to noncommutativity is just a time delay. This result is verified in two different ways. But the off-shell Green's functions do depend on ${\theta }_{\mu \nu }$. In the course of this analysis, unitarity of the non-perturbative S-matrix is proved as well.

18 pages, minor corrections, To appear in Phys. Rev. D, 2011

References in corpus (17)

• A Gravity Theory on Noncommutative Spaces
• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry
• Constraints from CMB on Spacetime Noncommutativity and Causality Violation
• Progress in solving a noncommutative quantum field theory in four dimensions
• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Quantum Fields on the Groenewold-Moyal Plane
• Twisted Poincaré Invariant Quantum Field Theories
• Non-Pauli Transitions From Spacetime Noncommutativity
• Non-Pauli Effects from Noncommutative Spacetimes
• Causality and statistics on the Groenewold-Moyal plane
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
• Thermofield dynamics and twisted Poincaré symmetry on Moyal space-time
• Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
• Spontaneous Symmetry Breaking in Twisted Noncommutative Quantum Theories
• Covariant Quantum Fields on Noncommutative Spacetimes

Cited by in corpus (5)

• Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
• UV/IR mixing as a twisted Poincaré anomaly
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• Twisted bosonization in two dimensional noncommutative spacetime
• Renormalization of Noncommutative Quantum Field Theories