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  • Letter
  • Open Access

Quantum field theory for classical fields

Christof Wetterich*

  • *Contact author: c.wetterich@thphys.uni-heidelberg.de
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APS Open Sci. 1, L000179 – Published 21 October, 2026

DOI: https://doi.org/10.1103/wnpq-hbpq

Abstract

For classical field theories with probabilistic initial conditions, the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial fluctuations. We propose to employ observables based on fluctuating fields. In terms of these “statistical observables,” the probabilistic classical field theory becomes a quantum field theory. Noncommuting operators are associated with observables. The quantum rules follow from the laws for classical probabilities. The “quantum” is part of the “classical.” A regularized functional integral guarantees the unitarity of the quantum field theory. We discuss in detail the classical relativistic Klein-Gordon equation with interactions.

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APS Open Sci. 1, L000179– Published 21 October, 2026
Vol. 1
  • Received 27 March 2026
  • Accepted 7 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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