Fermions from classical statistics

Abstract

We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities $p_{\tau }$ amounts to a rotation of the wave function $q_{\tau }(t)=\pm \sqrt{p_{\tau }(t)}$, we infer the unitary time evolution of a quantum system of fermions according to a Schrödinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

extended version with two new sections on symmetries 25 pages

References in corpus (2)

• Quantum mechanics from classical statistics
• Quantum particles from coarse grained classical probabilities in phase space

Cited by in corpus (9)

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• Fermions as generalized Ising models
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• Probabilistic time
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• Quantum fermions and quantum field theory from classical statistics