English

Hadamard renormalization for a charged scalar field

General Relativity and Quantum Cosmology 2020-04-08 v2 High Energy Physics - Theory

Abstract

The Hadamard representation of the Green's function of a quantum field on a curved space-time is a powerful tool for computations of renormalized expectation values. We study the Hadamard form of the Feynman Green's function for a massive charged complex scalar field in an arbitrary number of space-time dimensions. Explicit expressions for the coefficients in the Hadamard parametrix are given for two, three and four space-time dimensions. We then develop the formalism for the Hadamard renormalization of the expectation values of the scalar field condensate, current and stress-energy tensor. These results will have applications in the computation of renormalized expectation values for a charged quantum scalar field on a charged black hole space-time, and hence in addressing issues such as the quantum stability of the inner horizon.

Keywords

Cite

@article{arxiv.1910.03666,
  title  = {Hadamard renormalization for a charged scalar field},
  author = {Visakan Balakumar and Elizabeth Winstanley},
  journal= {arXiv preprint arXiv:1910.03666},
  year   = {2020}
}

Comments

31 pages, new section comparing with other approaches to renormalization, minor edits

R2 v1 2026-06-23T11:38:05.190Z