Wetterich, C. Fermions from classical statistics. (English) Zbl 1206.81117 Ann. Phys. 325, No. 12, 2750-2786 (2010). Summary: 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. Cited in 5 Documents MSC: 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 82B05 Classical equilibrium statistical mechanics (general) 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:quantum theory from classical statistics; fermions from Ising models; two-dimensional QFT for fermions; Grassmann functional integral PDFBibTeX XMLCite \textit{C. Wetterich}, Ann. Phys. 325, No. 12, 2750--2786 (2010; Zbl 1206.81117) Full Text: DOI arXiv References: [1] Wetterich, C., J. Phys., 174, 012008 (2009) [2] C. Wetterich, <arXiv:1002.2593>.; C. Wetterich, <arXiv:1002.2593>. [3] Wetterich, C., Ann. Phys., 325, 1359 (2010) [4] von Neumann, J., Ann. Math., 33, 789 (1932) [5] Coleman, S., Phys. Rev., D11, 2088 (1975) [6] Wetterich, C., Phys. Rev. Lett., 94, 011602 (2005) [7] Zinn-Justin, J., Quantum Field Theory and Critical Phenomena (1989), Oxford University Press [8] C. Wetterich, <arXiv:1005.3972>.; C. Wetterich, <arXiv:1005.3972>. [9] Keldysh, L. V., JETP, 20, 1018 (1965) [10] Osterwalder, K.; Schrader, R., Commun. Math. Phys., 42, 281 (1975) [11] C. Wetterich, <arXiv:1002.3556>.; C. Wetterich, <arXiv:1002.3556>. [12] Wetterich, C., Nucl. Phys., B211, 177 (1983) [13] Wetterich, C., (Elze, T., Decoherence and Entropy in Complex Systems (2004), Springer-Verlag), 180 [14] Bell, J. S., Physica, 1, 195 (1964) [15] Clauser, J.; Shimony, A., Rep. Prog. Phys., 41, 1881 (1978) [16] N. Straumann, <arXiv:0801.4931>.; N. Straumann, <arXiv:0801.4931>. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.