In this paper the Feynman Green function for Maxwell’s theory in curved spacetime is studied by using the Fock–Schwinger–DeWitt asymptotic expansion; the pointsplitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.

Divergent part of the stress-energy tensor for Maxwell's theory in curved space-time: a systematic derivation / Niardi, R; Esposito, G; Tramontano, F. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 136:5(2021), pp. 473-1-473-32. [10.1140/epjp/s13360-021-01403-1]

Divergent part of the stress-energy tensor for Maxwell's theory in curved space-time: a systematic derivation

ESPOSITO G
Secondo
;
2021

Abstract

In this paper the Feynman Green function for Maxwell’s theory in curved spacetime is studied by using the Fock–Schwinger–DeWitt asymptotic expansion; the pointsplitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.
2021
Divergent part of the stress-energy tensor for Maxwell's theory in curved space-time: a systematic derivation / Niardi, R; Esposito, G; Tramontano, F. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 136:5(2021), pp. 473-1-473-32. [10.1140/epjp/s13360-021-01403-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/841322
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