Real alternative to quantum gravity in loop space
Open accessAbstract
We show that the Hamiltonian constraint of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its nonpolynomiality possesses a natural quantum analogue in a lattice-discretized formulation of the theory. This opens the way for a systematic search of its zero eigenvectors. The unambiguous and well-defined kinematical scalar product is that of the SU(2)-gauge theory. We also comment on various aspects of the continuum theory.
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Physical and mathematical arguments indicate that this representation is relevant at the diffeomorphism-invariant and background-independent level.
“But physical and mathematical arguments indicate that this representation is relevant at the diffeomorphism-invariant and background-independent level [6,7].”
From Immirzi parameter in quantum general relativity (1998) · cites this paper as [7]
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Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · cited 2× · see citing works
“The Hamiltonian constraint function in terms of (A,E) reads ǫijkEai E b jF k ab − ( 2 β2 + 2)E [a i E b] j (A i a − Γia)(Ajb − Γ j b).”
Baez, J. C. (1996) · Advances in Mathematics · doi:10.1006/aima.1996.0012 · Cited by 266 · see citing works
Knot invariants as nondegenerate quantum geometries
Brügmann, B., Gambini, R., & Pullin, J. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.431 · Cited by 94 · see citing works
Spectrum of the volume operator in quantum gravity
Loll, R. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00627-3 · Cited by 90 · see citing works
Self-citationNon-perturbative solutions for lattice quantum gravity
Loll, R. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00184-t · Cited by 47 · see citing works
Self-citationGeneralized Wick transform for gravity
Ashtekar, A. (1996) · Physical Review D · doi:10.1103/physrevd.53.r2865 · Cited by 47 · see citing works
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Research works printed but not linked: 2
- [6][6] S. Holst: Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action, Stockholm U. preprint USITP-95-10 -
- [15][15] R. De Pietri and C. Rovelli: Geometry eigenvalues and scalar product from recoupling theory in loop quantum gravity, Parma U. preprint UPRF 96-444 -
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Simplifying the spectral analysis of the volume operator
Loll, R. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00334-9 · Cited by 27 · see citing works
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- Authors
- Loll, R.
- Affiliations
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze (IT)
- Corresponding author
- Loll, R.
- ORCID
- Loll, R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1996-10-15
- Volume
- 54
- Issue
- 8
- Pages
- 5381-5384
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2158823455
- Cited by
- 19
- References
- 6
- Citations by year
- 2017: 2
- FWCI
- 4.77
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- arXiv (Cornell University)
- 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 › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- loop quantum gravity, Hamiltonian constraint, SU(2) connection, lattice discretization
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