Causality in Non-Commutative Quantum Field Theories

Details Causality in Non-Commutative Quantum Field Theories Causality in Non-Commutative Quantum Field Theories

2007-01-18

arxiv.org/abs/hep-th/0701171v3

J.Phys.A41:215402,2008

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LaTeX; A few changes in sections 3.2,3.3 and 4

Scientific paper

10.1088/1751-8113/41/21/215402

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 $\bar{\psi}(x)\star\psi(x)\star\phi(x)$, is observed to be causality violating even in case of space-space noncommutativity for which \theta^{0i}=0. \

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