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

TL;DR

This paper studies the one-loop renormalization of the energy-momentum tensor in noncommutative  scalar field theory, showing how to construct finite, improved operators and calculating the mixing matrix explicitly.

Contribution

It provides a detailed construction of renormalized composite operators and the energy-momentum tensor in noncommutative  theory, including explicit mixing matrix calculations.

Findings

The bare composite operators are expressed via renormalized ones using a mixing matrix.

The canonical energy-momentum tensor is not finite and requires improvement.

Explicit form of the mixing matrix differs from the commutative case.

Abstract

We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative \phi^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.