Fermion Doubling in Loop Quantum Gravity
arXiv:1507.01232
Abstract
In this paper, we show that the Hamiltonian approach to loop quantum gravity has a fermion doubling problem. To obtain this result, we couple loop quantum gravity to a free massless scalar and a chiral fermion field, gauge fixing the many fingered time gauge invariance by interpreting the scalar field as a physical clock. We expand around a quantum gravity state based on a regular lattice and consider the limit where the bare cosmological constant is large but the fermonic excitations have energies low in Planck units. We then make the case for identifying the energy spectrum in this approximation with that of a model of lattice fermion theory which is known to double.
References in corpus (16)
- Quantum Spin Dynamics (QSD)
- Spin Networks and Quantum Gravity
- Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
- Quantum Spin Dynamics (QSD) II
- Algebraic Quantum Gravity (AQG) I. Conceptual Setup
- Gravity quantized
- The geometry of quantum spin networks
- Fermions in Quantum Gravity
- Domain Wall Fermions and Chiral Gauge Theories
- Coarse graining free theories with gauge symmetries: the linearized case
- Hamiltonian operator for loop quantum gravity coupled to a scalar field
- A dialog on quantum gravity
- Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
- No fermion doubling in quantum geometry
- Positive energy in quantum gravity
- Tata lectures on overlap fermions