Renormalization of the energy-momentum tensor in noncommutative scalar field theory

Abstract

We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative ϕ^4 scalar field theory. Proper operator bases are constructed and it is proved that the bare composite operators are expressed via renormalized ones, with the help of a mixing matrix, whose explicit form is calculated. The corresponding matrix elements turn out to differ from the commutative theory. The canonically defined energy-momentum tensor is not finite and must be replaced by the "improved" one, in order to provide finiteness. The suitable "improving" terms are found.

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• Noncommutative Quantum Scattering in a Central Field
• Noncommutative fluid dynamics in the Snyder space-time
• On the energy-momentum tensor in Moyal space
• Noncommutative Coulombic Monopole
• Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory
• A Finite Energy-Momentum Tensor for the ${\varphi }^3$ theory in $6$ dimensions