Quantum mechanics and quantum field theory of a fermion system

CHRISTOF WETTERICH

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, noncommuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata.

Egon Marx

Lei Sun

Based on the axiom system of Yuanji Field Theory, this paper establishes the underlying alignment between the Yuanji Field and Quantum Field Theory (QFT), and constructs the complete ontological correspondence between them. It is proved that the Yuanji Field can serve as the fundamental physical ontology of QFT without contradicting its mature mathematical framework. Starting from the Phase Single-valuedness Axiom and topological constraints of the Yuanji Field, the core framework of QFT is endogenously derived, including canonical quantization rules, field operators, Hamiltonian, and the statistical properties of fermions and bosons. Theoretical calculations on the first-order correction of the electron anomalous magnetic moment, Compton scattering cross-section, and Casimir effect are in good agreement with the classical results of Quantum Electrodynamics (QED) and experimental measurements. This work provides a continuous-field-dynamics-based interpretive perspective for quantum mechanics, and realizes the self-consistent unification of classical field theory, relativity, and quantum mechanics under a single axiom system.

Edwin Langmann A

Felix Finster, Johannes Kleiner

The theory of causal fermion systems is an approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. We here give a non-technical introduction.