Causality in Non-Commutative Quantum Field Theories
arXiv:hep-th/0701171 · doi:10.1088/1751-8113/41/21/215402
Abstract
We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian , is observed to be causality violating even in case of space-space noncommutativity for which θ^{0i}=0. \
arXiv comment18 pages, LaTeX; A few changes in sections 3.2,3.3 and 4
References in corpus (12)
- String Theory and Noncommutative Geometry
- Quantum Field Theory on Noncommutative Spaces
- The quantum structure of spacetime at the Planck scale and quantum fields
- Space/Time Non-Commutativity and Causality
- General Properties of Noncommutative Field Theories
- Spin-Statistics and CPT Theorems in Noncommutative Field Theory
- Remarks on Time-Space Noncommutative Field Theories
- Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
- Failure of microcausality in quantum field theory on noncommutative spacetime
- Causality Violation in Non-local Quantum Field Theory
- Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory
- Perturbation theory of the space-time non-commutative real scalar field theories