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Fermion coupling to loop quantum gravity: canonical formulation
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In the model of a fermion field coupled to loop quantum gravity, we consider the Gauss and the Hamiltonian constraints. According to the explicit solutions to the Gauss constraint, the fermion spins and the gravitational spin networks intertwine with each other so that the fermion spins contribute to the volume of the spin network vertices. For the Hamiltonian constraint, the regularization and quantization procedures are presented in detail. By introducing an adapted vertex Hilbert space to remove the regulator, we propose a diffeomorphism covariant graph-changing Hamiltonian constraint operator of the fermion field. This operator shows how fermions move in the loop quantum gravity spacetime and simultaneously influences the background quantum geometry.
Forward citations
Cited by 2 Pith papers
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An inquiry on the Absence of Fermion Doubling and why the Nielsen-Ninomiya Theorem Does Not Apply to Nonlocal Quantum Field Theory
A continuum nonlocal Dirac operator multiplied by an invertible zero-free entire function has exactly the same kernel and finite-momentum zero set as the ordinary Dirac operator, so fermion doubling is absent.
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Bell states for fermions in loop quantum gravity
In loop quantum gravity, a surface-normal fermion spin observable can be used to construct CHSH-type correlations that are violated by fermion states coupled to quantum geometry.
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