Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

TL;DR

This paper develops a comprehensive Hadamard renormalization framework for the stress-energy tensor of a massive scalar field in arbitrary-dimensional spacetimes, aiding quantum physics studies in higher dimensions.

Contribution

It provides explicit procedures for dimensions up to six and a general framework for dimensions seven to eleven, including ambiguity analysis and counterterm expressions.

Findings

Explicit Hadamard renormalization procedures for dimensions up to six.

Framework for performing renormalization in dimensions seven to eleven.

Analysis of ambiguities and counterterms in the renormalization process.

Abstract

We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimension up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimension from seven to eleven, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.