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Cited by 4Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesRelativity and Gravitational Theory

The DOI matches its Crossref record.

Functional approach to (2 1)-dimensional gravity coupled to particles

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Cantini, Luigi, Menotti, Pietro·2003·Classical and Quantum Gravity
DOI 10.1088/0264-9381/20/5/305
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Abstract

The quantum gravity problem of point particles interacting with the gravitational field in 2 + 1 dimensions is approached by working out the phase-space functional integral. The maximally slicing gauge is adopted for a non-compact open universe with the topology of the plane. The momenta conjugate to the gravitational field are related to a class of meromorphic quadratic differentials. The boundary term for the non-compact space is worked out in detail. In the extraction of the physical degrees of freedom functional determinants related to the puncture formulation of string theory occur and cancel out in the final reduction. Finally, the ordering problem in the definition of the functional integral is discussed.

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  • The phase space path integral for spatially closed universes and for geometries with point particles is equivalent to canonical quantization of Section 3.1.

    “This is indeed true, as shown in [77, 245] for spatially closed universes and [63] for geometries with point particles.”

    From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [63]

    For geometries with point particles, the paper derives a phase-space functional integral with the same expression as reduced particle dynamics (Additional information, eq. 71). But it says the resulting integral does not resolve operator ordering and that the relationship between the functional and operator approaches remains unclear (p. 846; §5). It therefore does not establish unqualified equivalence to canonical quantization. The spatially closed-universe part is attributed to other citations, not this paper. (LLM, conf=0.86)

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Metadata

Authors
Cantini, L., & Menotti, P.
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2003-02-14
Volume
20
Issue
5
Pages
845-857
ISSN
0264-9381 (ISSN-L)
DOI
10.1088/0264-9381/20/5/305
OpenAlex
W2073774638
Cited by
4
References
0
Citations by year
2014: 1
FWCI
0.48
Type
journal article
Language
en
Open access
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
Ministero dell’Istruzione, dell’Università e della Ricerca
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
three-dimensional gravity, point particles, meromorphic quadratic differentials, boundary terms, string theory, functional determinants, ordering problem, quantum gravity

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