QFT with Twisted Poincaré Invariance and the Moyal Product

Abstract

We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.

11 pages, references added

References in corpus (10)

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Cited by in corpus (11)

• Fock space, quantum fields and kappa-Poincaré symmetries
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Braided quantum field theories and their symmetries
• Noncommutative fields and actions of twisted Poincare algebra
• Duality and Braiding in Twisted Quantum Field Theory
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Wedge locality and asymptotic commutativity
• The Hilbert space of 3d gravity: quantum group symmetries and observables
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• On the Correspondence between Poincaré Symmetry of Commutative QFT and Twisted Poincaré Symmetry of Noncommutative QFT