On general properties of Lorentz invariant formulation of noncommutative quantum field theory

Abstract

We study general properties of certain Lorentz invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge causality condition. This is the consequence of the infinite nonlocality of the theory getting spread in all spacetime directions. We also show that the time-ordered perturbation theory arising from the Hamiltonian formulation of noncommutative quantum field theories remains inequivalent to the covariant perturbation theory with usual Feynman rules even after restoration of Lorentz symmetry.

13 pages, references added

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• Fermions and noncommutative theories
• Quantum complex scalar fields and noncommutativity
• Tensor Coordinates in Noncommutative Mechanics
• A New Limit for the Non-Commutative Space-Time Parameter
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• The Strong Interaction Model in DFR noncommutative space-time
• Microcausality of spin-induced noncommutative theories
• Casimir effect in DFR space-time
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
• The standard electroweak model in the noncommutative $DFR$ space-time