Regularization and finiteness of the Lorentzian loop quantum gravity vertices
Open accessAbstract
We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of doing so, a natural regularization of the vertices is suggested. The regularized vertices are then proven to be finite. An interpretation of the regularization in terms of a gauge fixing is also given.
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The Lorentzian EPRL vertex amplitude is divergent because of a redundant SL(2,C) integration, and it becomes finite when one arbitrary integration is removed.
“The vertex amplitude is divergent due to the presence of a redundant integration over SL(2, ℂ), it becomes finite by dropping an arbitrary integration, i.e., removing any of the 5 boxes in the vertex expression [167].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [167]
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- Authors
- Engle, J., & Pereira, R.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- ORCID
- Engle, Jonathan
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2009-04-23
- Volume
- 79
- Issue
- 8
- Pages
- 084034
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2117180421
- Cited by
- 63
- References
- 34
- Citations by year
- 2026: 4 · 2025: 1 · 2024: 3 · 2023: 5 · 2022: 2 · 2021: 2 · 2020: 1 · 2019: 1 · 2018: 2 · 2017: 1 · 2016: 5 · 2015: 1 · 2014: 3 · 2013: 10 · 2012: 11
- FWCI
- 5.05
- 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)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- 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, regularization, finiteness, gauge fixing, simplicial quantum gravity
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