DeWitt-Schwinger renormalization and vacuum polarization in d dimensions

Journal Article · Tue Sep 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.064017· OSTI ID:21322730

Thompson, R T ^[1]; Lemos, Jose P. S. ^[1]

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1. Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal)

Calculation of the vacuum polarization, <{phi}{sup 2}(x)>, and expectation value of the stress tensor, <T{sub {mu}}{sub {nu}}(x)>, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to d dimensions includes d-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for <{phi}{sup 2}(x)> and <T{sub {mu}}{sub {nu}}(x)> calculations and a thorough introduction to the method of calculating <{phi}{sup 2}(x)>, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of <{phi}{sup 2}(x)> and <T{sub {mu}}{sub {nu}}(x)> in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to <{phi}{sup 2}(x)> for certain spacetimes is discussed, with application to four and five dimensions.

• OSTI ID: 21322730
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BLACK HOLES
EXPANSION
EXPECTATION VALUE
FOUR-DIMENSIONAL CALCULATIONS
MANY-DIMENSIONAL CALCULATIONS
RENORMALIZATION
SIMULATION
SPACE-TIME
STRESSES
TENSORS
VACUUM POLARIZATION