SQG5 - Quantum Fields |
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Speaker |
Thompson, Robert |
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Co-autors |
J.P.S. Lemos |
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Talk Title |
DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions |
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Abstract |
Calculation of the vacuum polarization, $\langle\phi^2(x)\rangle$, and expectation value of the stress tensor, $\langle T_{\mu\nu}(x)\rangle$, 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 a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even dimensional spacetimes is presented. This formula should be useful for calculations of $\langle\phi^2(x)\rangle$ and $\langle T_{\mu\nu}(x)\rangle$ 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 $\langle\phi^2(x)\rangle$ for certain spacetimes is discussed, with application to four and five dimensions. |
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