A novel method for renormalization in quantum-field theory in curved spacetime

Abstract

In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor [Formula: see text] and of the square of the field operator [Formula: see text]. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of [Formula: see text] for a massless scalar field in Bertotti–Robinson spacetime.

Quantum field theory on global anti-de Sitter space-time with Robin boundary conditions

“…In other words, rather than express the Feynman Green's function in closed form and subtract the local Hadamard parametrix, we express the local Hadamard parametrix as a mode-sum and subtract from the Feynman Green's function mode-by-mode. While there are several recently-developed methods for achieving this in principle (see, for example, [52][53][54][55][56]), these methods are difficult to implement in the present situation since the mode-sum representation of the Hadamard parametrix is insensitive to the field boundary conditions and therefore the frequencies of such a decomposition are not those coming from the quantization condition (2.10).…”

Quantum field theory on global anti-de Sitter space-time with Robin boundary conditions

“…In other words, rather than express the Feynman Green's function in closed form and subtract the local Hadamard parametrix, we express the local Hadamard parametrix as a mode-sum and subtract from the Feynman Green's function mode-by-mode. While there are several recently-developed methods for achieving this in principle (see, for example, [50][51][52][53][54]), these methods are difficult to implement in the present situation since the mode-sum representation of the Hadamard parametrix is insensitive to the field boundary conditions and therefore the frequencies of such a decomposition are not those coming from the quantization condition (2.10).…”

Vacuum polarization on topological black holes with Robin boundary conditions

“…In the past five years, new approaches to computations of the VP and RSET for a quantum scalar field have been developed [30][31][32]. The "extended coordinates" method of Taylor and Breen [31,33,34], like the AHS method, involves a Euclideanized spacetime and will be the method adopted here.…”