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Abstract The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity (LQG). As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of LQG, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in LQG. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity.
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Key Issues Review: A short review of loop quantum gravity
An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of GR: gravity is a manifestation of spacetime geometry. Thus, the approach emphasizes the quantum nature of geometry and focuses on its implications in extreme regimes—near the big bang and inside black holes—where Einstein’s smooth continuum breaks down.We present a brief overview of the main ideas underlying LQG and highlight a few recent advances. This report is addressed to non-experts.
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- Award ID(s):
- 1806356
- PAR ID:
- 10280385
- Date Published:
- Journal Name:
- Reports on progress in physics
- Volume:
- 84
- Issue:
- 042001
- ISSN:
- 0034-4885
- Page Range / eLocation ID:
- 1-19
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/https://doi.org/10.1088/1361-6633/abed91
