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1997 | 39 | 1 | 331-344
Tytuł artykułu

Refined Algebraic Quantization: Systems with a single constraint

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While in general the results depend heavily on the choices made for certain auxiliary structures, an additional physical argument leads to a unique result for typical cases. We also discuss the 'superselection laws' that result from this scheme and how their existence also depends on the choice of auxiliary structures. Again, when these structures are chosen in a physically motivated way, the resulting superselection laws are physically reasonable.
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
331-344
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Physics Department, University of California Santa Barbara, California 93106, USA
Bibliografia
  • [1] A. Ashtekar, Non-Perturbative Canonical Gravity, Lectures notes prepared in collaboration with R. S. Tate, World Scientific, Singapore, 1991.
  • [2] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom, J. Math. Phys. 36 (1995), 6456-6493; gr-qc/9504018.
  • [3] A. Ashtekar and R. S. Tate, An algebraic extension of Dirac quantization: Examples, J. Math. Phys. 35 (1994), 6434-6470.
  • [4] B. DeWitt, Quantum Theory of Gravity. I: The Canonical Theory, Phys. Rev. (2) 160 (1967), 1113-1148.
  • [5] P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University, New York, 1964.
  • [6] I. M. Ge{l'fand, N. Ya. Vilenkin, Generalized Functions: vol. 4, Applications of Harmonic Analysis, Academic Press, New York, London, 1964.
  • [7] P. Hájíček, Quantization of Systems with Constraints, in: Canonical Gravity: from classical to quantum, J. Ehlers, H. Friedrich (eds.), Lecture Notes in Phys. 434, Springer, Berlin, 1994, 113-149.
  • [8] A. Higuchi, Quantum linearization instabilities of de Sitter spacetime: II, Classical Quantum Gravity 8 (1991), 1983-2004.
  • [9] A. Higuchi, Linearized quantum gravity in flat space with toroidal topology, Classical Quantum Gravity 8 (1991), 2023-2034.
  • [10] C. Isham, Canonical Gravity and the Problem of Time, Imperial College, preprint TP/91-92/25; gr-qc/9210011, 1992.
  • [11] K. Kuchař, Time and Interpretations of Quantum Gravity, in: Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, G. Kunstatter et al. (eds.), World Scientific, New Jersey, 1992, 211-314.
  • [12] N. Landsman, Rieffel induction as generalized quantum Marsden-Weinstein reduction, J. Geom. Phys. 15 (1995), 285-319; hep-th/9305088. Erratum: ibid. 17 (1995), 298.
  • [13] N. Landsman, Classical and quantum representation theory, in: Proceedings Seminar Mathematical Structures in Field Theory, E. A. de Kerf and H. G. J. Pijls (eds.), CWI-syllabus, CWI, Amsterdam, to appear.
  • [14] N. Landsman and U. Wiedemann, Massless Particles, Electromagnetism, and Rieffel Induction, Rev. Math. Phys. 7 (1995), 923-958; hep-th/9411174.
  • [15] D. Marolf, The spectral analysis inner product for quantum gravity, preprint gr-qc/9409036, to appear in the Proceedings of the VIIth Marcel-Grossman Conference, R. Ruffini and M. Keiser (eds.), World Scientific, Singapore, 1995.
  • [16] D. Marolf, Green's Bracket Algebras and their Quantization, Ph. D. Dissertation, The University of Texas at Austin, 1992.
  • [17] D. Marolf, Quantum observables and recollapsing dynamics, Classical Quantum Gravity 12 (1995), 1199-1220; gr-qc/9404053.
  • [18] D. Marolf, Observables and a Hilbert Space for Bianchi IX, Classical Quantum Gravity 12 (1995), 1441-1454; gr-qc/9409049.
  • [19] D. Marolf, Almost Ideal Clocks in Quantum Cosmology: A Brief Derivation of Time, Classical Quantum Gravity 12 (1995), 2469-2486; gr-qc/9412016.
  • [20] B. Simon, Quantum Mechanics for Hamiltonians defined as quadratic forms, Princeton Univ. Press, Princeton, 1971, p. 120.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv39z1p331bwm
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