The classical evaluation of relativistic spin networks
Open accessAbstract
The evaluation of a relativistic spin network for the classical case of the Lie group is given by an integral formula over copies of SU(2).For the graph determined by a 4-simplex this gives the evaluation as an integral over a space of geometries for a 4-simplex.
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A field theory over a group formulation can be given for the Lorentzian Barrett-Crane model using both realizations of simple representations on Q1 and Q-1.
“A field theory over group formulation can also be given for the Lorentzian Barrett-Crane model [102,103], using both realizations of the simple representations on Q 1 and Q -1 .”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [102]
The relevant Barrett-Crane models use the Q1 realization, involving only spacelike (0,ρ) representations, and the Q-1 realization, involving both timelike (j,0) and spacelike (0,ρ) representations; the first was developed in [34,102] and the second in [103].
“The relevant Barrett-Crane models are those using the realizations on Q 1 , which involves only spacelike representations of the type (0, ρ), and Q -1 , which instead involves both timelike (j, 0) and spacelike (0, ρ) representations.The first case was developed in [34,102], while the second one appeared in [103].”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [102]
In the Q1 case the amplitude is given by formula (113) from [102,103].
“In the first case (Q 1 ) the amplitude is given by [102,103]”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [102]
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References 4 · Cited by 60
Research works printed but not linked: 1
- J. W. Barrett and B. W. Westbury, Trans. A. M. S. 348 (1996) 3997.
- Authors
- Barrett, J. W.
- Affiliations
- University of Nottingham (GB)
- Corresponding author
- Barrett, John W.
- Venue
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Published
- 1998
- Volume
- 2
- Issue
- 3
- Pages
- 593-600
- ISSN
- 1095-0753 (ISSN-L)
- 1095-0761
- OpenAlex
- W2149468928
- Cited by
- 60
- References
- 4
- Citations by year
- 2015: 1 · 2013: 2 · 2012: 5
- FWCI
- 5.68
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Theoretical and Mathematical Physics (publishedVersion)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- Repository@Nottingham (University of Nottingham) (submittedVersion, other-oa)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- SU(2), 4-simplex, integral formulas, quantum gravity, Regge calculus
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