Probabilistic cellular automata for interacting fermionic quantum field theories
arXiv:2007.06366 · doi:10.1016/j.nuclphysb.2020.115296
Abstract
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.
arXiv commentAdditional clarifications, 14 pages, 5 figures
References in corpus (11)
- Emergence of quantum mechanics from classical statistics
- Quantum mechanics from classical statistics
- Quantumness of discrete Hamiltonian cellular automata
- Quantum particles from classical statistics
- Quantum formalism for classical statistics
- Fermions from classical statistics
- On the solution of the massless Thirring model with fermion fields quantized in the chiral symmetric phase
- Fermions as generalized Ising models
- Probabilistic time
- Quantum field theory from classical statistics
- Static memory materials
Cited by in corpus (7)
- Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics
- Pregeometry and spontaneous time-space asymmetry
- Fermionic quantum field theories as probabilistic cellular automata
- Quantum fermions from classical bits
- Are Quantum-Classical Hybrids compatible with Ontological Cellular Automata?
- Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
- Hierarchy of percolation patterns in a kinetic replication model