Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field

Abstract

We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger and adiabatic) to the renormalization of expectation values of field operators acting on a charged quantum scalar field. First, we demonstrate that the DeWitt-Schwinger representation of the Feynman Green's function is a particular case of the Hadamard representation. Next, we restrict attention to a spatially flat Friedmann-Lemaitre-Robertson-Walker universe with time-dependent, purely electric, background electromagnetic field, considering two, three and four-dimensional space-times. Working to the order required for the renormalization of the stress-energy tensor (SET), we find the adiabatic and DeWitt-Schwinger expansions of the Green's function when the space-time points are spatially separated. In two and four dimensions, the resulting DeWitt-Schwinger and adiabatic expansions are identical. In three dimensions, the DeWitt-Schwinger expansion contains terms of adiabatic order four which are not necessary for the renormalization of the SET and hence absent in the adiabatic expansion. The equivalence of the DeWitt-Schwinger and adiabatic approaches to renormalization in the scenario considered is thereby demonstrated in even dimensions. In odd dimensions the situation is less clear and further investigation is required in order to determine whether adiabatic renormalization is a locally covariant renormalization prescription.

arXiv comment23 pages, no figures, minor changes, version accepted for publication in Physical Review D

References in corpus (26)

• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Quantum fields in curved spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• Adiabatic regularization and particle creation for spin one-half fields
• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
• Adiabatic regularization for spin-1/2 fields
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
• Particle creation and particle number in an expanding universe
• On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes - Comparison of Different Regularization Schemes and Symmetry of the Hadamard/Seeley-DeWitt Coefficients
• Adiabatic expansions for Dirac fields, renormalization, and anomalies
• Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect
• Equivalence of Adiabatic and DeWitt-Schwinger renormalization schemes
• Pair creation in electric fields, anomalies, and renormalization of the electric current
• Role of gravity in the pair creation induced by electric fields
• Adiabatic regularization with a Yukawa interaction
• Renormalization of the charged scalar field in curved space
• Hadamard renormalization for a charged scalar field
• Adiabatic regularization for Dirac fields in time-varying electric backgrounds
• A method for calculating the imaginary part of the Hadamard Elementary function $G^{(1)}$ in static, spherically symmetric spacetimes
• Note on the pragmatic mode-sum regularization method: translational-splitting in a cosmological background
• Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
• R-summed form of adiabatic expansions in curved spacetime
• Hadamard Renormalization of a 2-Dimensional Dirac Field

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