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Titolo:
Gauge field theory coherent states (GCS): II: Peakedness properties
Autore:
Thiemann, T; Winkler, O;
Indirizzi:
MPI Gravitat Phys, Albert Einstein Inst, D-14476 Golm, Germany MPI Gravitat Phys Golm Germany D-14476 stein Inst, D-14476 Golm, Germany
Titolo Testata:
CLASSICAL AND QUANTUM GRAVITY
fascicolo: 14, volume: 18, anno: 2001,
pagine: 2561 - 2636
SICI:
0264-9381(20010721)18:14<2561:GFTCS(>2.0.ZU;2-7
Fonte:
ISI
Lingua:
ENG
Soggetto:
SPIN DYNAMICS QSD; CANONICAL QUANTUM-GRAVITY; GENERAL-RELATIVITY; VOLUME OPERATOR; BLACK-HOLE; LOOP-SPACE; STATISTICAL-MECHANICS; ASHTEKAR VARIABLES; REALITY CONDITIONS; SCALAR PRODUCT;
Tipo documento:
Review
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
114
Recensione:
Indirizzi per estratti:
Indirizzo: Thiemann, T MPI Gravitat Phys, Albert Einstein Inst, Muhlenberg 1, D-14476Golm, Germany MPI Gravitat Phys Muhlenberg 1 Golm Germany D-14476 , Germany
Citazione:
T. Thiemann e O. Winkler, "Gauge field theory coherent states (GCS): II: Peakedness properties", CLASS QUANT, 18(14), 2001, pp. 2561-2636

Abstract

In this paper we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state transform was introduced by Hall for one edge and generalized byAshtekar, Lewandowski, Marolf, Mourao and Thiemann to arbitrary, finite, piecewise-analytic graphs. However, both of these works were incomplete with respect to the followingtwo issues. (a) The focus was on the unitarity of the transform and left the properties of the corresponding coherent states themselves untouched. (b) While these states depend in some sense. on complexified connections, it remained unclear what the complexification was in terms of the coordinates of the underlying real phase space. In this paper we complement these results: first, we explicitly derive thecomplexification of the configuration space underlying these heat kernel coherent states and, secondly, prove that this family of states satisfies all the usual properties. (i) Peakedness in the configuration, momentum and phase space (or Bargmann-Segal) representation. (ii) Saturation of the unquenched Heisenberg uncertainty bound. (iii) (Over)completeness. These states therefore comprise a candidate family for the semiclassical analysis of canonical quantum gravity and quantum gauge theory coupled to quantum gravity. They also enable error-controlled approximations to difficult analytical calculations and therefore set a new starting point for numerical, semiclassical canonical quantum general relativity and gauge theory. The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.

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Documento generato il 08/04/20 alle ore 11:08:45