Fermionic quantum field theories as probabilistic cellular automata
arXiv:2111.06728 · doi:10.1103/PhysRevD.105.074502
Abstract
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two - dimensional quantum field theories for fermions. They can be viewed as generalized Ising models on a square lattice and therefore as classical statistical systems. As quantum field theories they are quantum systems. Thus quantum mechanics emerges from classical statistics. As an explicit example for an interacting fermionic quantum field theory we describe a type of discretized Thirring model as a cellular automaton. The updating rule of the automaton is encoded in the step evolution operator that can be expressed in terms of fermionic annihilation and creation operators. The complex structure of quantum mechanics is associated to particle -- hole transformations. The naive continuum limit exhibits Lorentz symmetry. We exploit the equivalence to quantum field theory in order to show how quantum concepts as wave functions, density matrix, non-commuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata.
arXiv commentClearer structure with focus on key points and appendices, 46 pages, 4 figures
References in corpus (18)
- Spinors in euclidean field theory, complex structures and discrete symmetries
- Emergence of quantum mechanics from classical statistics
- Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics
- Quantum mechanics from classical statistics
- Quantumness of discrete Hamiltonian cellular automata
- Probabilistic cellular automata for interacting fermionic quantum field theories
- Quantum particles from classical statistics
- Quantum formalism for classical statistics
- Quantum computing with classical bits
- On the solution of the massless Thirring model with fermion fields quantized in the chiral symmetric phase
- Fermions as generalized Ising models
- Fermions from classical statistics
- Classical probabilities for Majorana and Weyl spinors
- Probabilistic time
- Quantum fermions from classical bits
- Quantum field theory from classical statistics
- Emulating quantum computation with artificial neural networks
- Static memory materials