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Causality in Non-Commutative Quantum Field Theories

Asrarul Haque·Satish D. Joglekar
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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 $\barψ(x)\starψ(x)\starϕ(x)$, is observed to be causality violating even in case of space-space noncommutativity for which θ^{0i}=0. \

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Asrarul Haque, Satish D. Joglekar. 2007-03-03. Causality in Non-Commutative Quantum Field Theories. https://doi.org/10.1088/1751-8113%2F41%2F21%2F215402

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