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arXiv · 1910.03666

Hadamard renormalization for a charged scalar field

Visakan Balakumar·Elizabeth Winstanley
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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.

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Visakan Balakumar, Elizabeth Winstanley. 2019-10-08. Hadamard renormalization for a charged scalar field. https://doi.org/10.1088/1361-6382%2Fab6b6e

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