TOPOLOGICAL MEASURE AND GRAPH-DIFFERENTIAL GEOMETRY ON THE QUOTIENT SPACE OF CONNECTIONS
Open accessAbstract
Integral calculus on the space [Formula: see text] of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of [Formula: see text]. The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The definition of C [ N ] is plagued by ordering ambiguities.
“The definition of C [ N ] is plagued by ordering ambiguities [32,33,43].”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [32]
The ambiguity in the definition of C[N] was fixed in [32] and [33] to a large extent arbitrarily.
“Recall that the ambiguity in the definition of C [ N ] was fixed in [32] and [33] to a large extent arbitrarily.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [32]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Representation Theory of Analytic Holonomy C* Algebras
Ashtekar, A., & Lewandowski, J. (1993) · arXiv · doi:10.48550/arxiv.gr-qc/9311010 · Cited by 155 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 3
- [1]1. A. Ashtekar, Non-perturbative canonical quantum gravity (Notes prepared in collaboration with R.S. Tate), (World Scientific, Singapore, 1991).
- [2]2. A. Ashtekar, in: Proceedings of the 1992 Les Houches summer school on 'Gravitation and Quantization'
- [6]6. J. Baez, In: Proceedings of the conference on quantum topology (to appear, 1993)
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951 · see citing works
Self-citation(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · see citing works
Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory
Rovelli, C., & Vidotto, F. (2014) · doi:10.1017/cbo9781107706910 · Cited by 544 · see citing works
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Ashtekar, A., Lewandowski, J., Marolf, D., Mourão, J., & Thiemann, T. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531252 · Cited by 528 · see citing works
Self-citation(1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 412 · see citing works
Self-citation“Sum over surfaces” form of loop quantum gravity
Reisenberger, M. P., & Rovelli, C. (1997) · Physical Review D · doi:10.1103/physrevd.56.3490 · Cited by 372 · see citing works
Differential geometry on the space of connections via graphs and projective limits
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00028-g · Cited by 303 · see citing works
Self-citationCarlo Rovelli, C. (2006) · The frontiers collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 347 · see citing works
Baez, J. C. (1996) · Advances in Mathematics · doi:10.1006/aima.1996.0012 · Cited by 266 · see citing works
Coherent State Transforms for Spaces of Connections
Ashtekar, A., Lewandowski, J., Marolf, D. M., Mourão, J. M., & Thiemann, T. (1996) · Journal of Functional Analysis · doi:10.1006/jfan.1996.0018 · Cited by 104 · see citing works
Self-citationReality conditions inducing transforms for quantum gauge field theory and quantum gravity
Thiemann, T. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/6/012 · Cited by 102 · see citing works
Spin networks in nonperturbative quantum gravity
Baez, J. C. (1996) · Proceedings of symposia in applied mathematics · doi:10.1090/psapm/051/1372769 · Cited by 92 · see citing works
Reality conditions inducing transforms for quantum gauge field theory and quantum gravityPreprint
Thiemann, T., & Cgpg, P. (1995) · Cited by 77 · see citing works
On the Low-Energy Ramifications and a Mathematical Extension of Loop Quantum Gravity
Willis, J. L. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 81 · see citing works
Functional Integration on Spaces of Connections
Baez, J. C., & Sawin, S. (1997) · Journal of Functional Analysis · doi:10.1006/jfan.1997.3108 · Cited by 69 · see citing works
Matrix elements of Thiemann's Hamiltonian constraint in loop quantum gravity
Borissov, R., Pietri, R. D., & Carlo Rovelli, C. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/10/008 · Cited by 59 · see citing works
On the relation between the connection and the loop representation of quantum gravity
Pietri, R. D. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/009 · Cited by 50 · see citing works
Linking covariant and canonical LQG II: spin foam projector
Thiemann, T., & Zipfel, A. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/12/125008 · Cited by 36 · see citing works
Physical properties of quantum field theory measures
Mourão, J. M., Thiemann, T., & Velhinho, J. M. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532868 · Cited by 30 · see citing works
The inverse loop transformPreprint
Thiemann, T., & Cgpg, P. (1998) · Cited by 30 · see citing works
Carlo Rovelli, C. (2006) · AIP conference proceedings · doi:10.1063/1.2399564 · Cited by 29 · see citing works
Loop quantum gravity - a short reviewPreprint
Sahlmann, H. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1001.4188 · Cited by 31 · see citing works
Bouncing evolution in a model of loop quantum gravity
Zhang, C., Lewandowski, J., Li, H., & Ma, Y. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.124012 · Cited by 26 · see citing works
Self-citationBackground independent quantizations—the scalar field: I
Kamiński, W., Lewandowski, J., & Bobieński, M. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/9/001 · Cited by 27 · see citing works
Self-citationBackground independent quantizations—the scalar field: II
Kamiński, W., Lewandowski, J., & Okołów, A. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/18/005 · Cited by 24 · see citing works
Self-citationThiemann, T. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532344 · Cited by 24 · see citing works
Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
Zhang, C., Lewandowski, J., & Ma, Y. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.086014 · Cited by 18 · see citing works
Self-citationQuantum gravity as a “sum over surfaces”
Rovelli, C. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00351-4 · Cited by 18 · see citing works
How many quanta are there in a quantum spacetime?
Ariwahjoedi, S., Kosasih, J. S., Carlo Rovelli, C., & Zen, F. P. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/16/165019 · Cited by 11 · see citing works
A cohomological description of connections and curvature over posets
Roberts, J. E., & Ruzzi, G. (2006) · Theory and applications of categories · doi:10.70930/tac/90n4w15d · Cited by 11 · see citing works
Lewandowski, J., & Okołów, A. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3265923 · Cited by 8 · see citing works
Self-citationFermion coupling to loop quantum gravity: Canonical formulation
Lewandowski, J., & Zhang, C. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.124025 · Cited by 5 · see citing works
Self-citationConstrained projective quantum states for the degenerate Plebański gravity
Okołów, A. (2017) · Journal of Mathematical Physics · doi:10.1063/1.4990792 · Cited by 1 · see citing works
Review on hermiticity of the volume operators in Loop Quantum Gravity
Ariwahjoedi, S., Belfaqih, I. H., Sebastian, I., & Zen, F. P. (2019) · General Relativity and Gravitation · doi:10.1007/s10714-019-2541-2
This Week's Finds in Mathematical Physics (1-50)Preprint
Baez, J. C. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.04168
- Authors
- LEWANDOWSKI, J.
- Affiliations
- University of Florida (US)
- Corresponding author
- LEWANDOWSKI, JERZY
- ORCID
- LEWANDOWSKI, JERZY
- Venue
- International Journal of Modern Physics D
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1994-03
- Volume
- 03
- Issue
- 01
- Pages
- 207-210
- ISSN
- 0218-2718 (ISSN-L)
- 1793-6594
- OpenAlex
- W2102370110
- Cited by
- 36
- References
- 1
- Citations by year
- 2022: 1 · 2021: 1 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2014: 2
- FWCI
- 7.20
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- International Journal of Modern Physics D (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- cylindrical measures, topological vector spaces, momentum operator, gauge theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
