DeWitt-Schwinger renormalization and vacuum polarization in d dimensions
- 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, Vol. 80, Issue 6; Other Information: DOI: 10.1103/PhysRevD.80.064017; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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