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The dimensional-reduction anomaly.

Sutton, Patrick James.

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The dimensional-reduction anomaly.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The dimensional-reduction anomaly./
Author:	Sutton, Patrick James.
Description:	157 p.
Notes:	Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2351.
Contained By:	Dissertation Abstracts International62-05B.
Subject:	Physics, General. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ59681
ISBN:	0612596818

The dimensional-reduction anomaly.
Sutton, Patrick James.

The dimensional-reduction anomaly. - 157 p.

Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2351.

Thesis (Ph.D.)--University of Alberta (Canada), 2000.

In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces. Substitution into the field equations reduces the free quantum field in D dimensions to a collection of quantum fields in D - n dimensions. This dimensional reduction establishes a formal relationship whereby objects in the physical theory, such as the Green function and the effective action, can be written as sums of the corresponding objects in the dimensionally reduced theories.

ISBN: 0612596818Subjects--Topical Terms:

1018488
Physics, General.

The dimensional-reduction anomaly.
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245 1 4 $a The dimensional-reduction anomaly.
300 $a 157 p.
500 $a Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2351.
500 $a Adviser: Valeri P. Frolov.
502 $a Thesis (Ph.D.)--University of Alberta (Canada), 2000.
520 $a In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces. Substitution into the field equations reduces the free quantum field in D dimensions to a collection of quantum fields in D - n dimensions. This dimensional reduction establishes a formal relationship whereby objects in the physical theory, such as the Green function and the effective action, can be written as sums of the corresponding objects in the dimensionally reduced theories.
520 $a In this thesis we examine dimensional reduction in the context of renormalization. Quantities of physical interest in quantum field theory, such as the expectation value of the stress tensor, are divergent and must be renormalized. Though the equivalence of the original and dimensionally-reduced theories is easily established at the bare level, we demonstrate that the divergent terms which must be subtracted to renormalize the higher- and lower-dimensional theories are not related by the mode decomposition. As a result, renormalized expectation values in D dimensions can be obtained by summing over their renormalized (D - n)-dimensional counterparts only if the contribution of each mode is modified by an extra anomalous contribution. We call this effect the dimensional-reduction anomaly.
520 $a We explicitly calculate the dimensional-reduction anomaly in the field fluctuations and the stress tensor for several classes of spacetimes of physical interest, with particular emphasis on spherical and static spaces. In each case, the anomaly is shown to produce significant mode-by-mode corrections to renormalized expectation values in the dimensionally reduced theories. For spherical geometries we investigate the relevance of the anomaly to recent attempts to calculate the stress tensor and Hawking radiation from Schwarzschild black holes using two-dimensional dilaton-gravity models. For static spaces we find an intriguing relationship between the anomaly and a new, general approximation scheme for renormalized expectation values of quantum fields.
590 $a School code: 0351.
650 4 $a Physics, General. $3 1018488
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710 2 0 $a University of Alberta (Canada). $3 626651
773 0 $t Dissertation Abstracts International $g 62-05B.
790 1 0 $a Frolov, Valeri P., $e advisor
790 $a 0351
791 $a Ph.D.
792 $a 2000
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ59681