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Electric field fluctuations and renormalization group flows in a self-interacting scalar field theory

Melanie Martínez Villarreal1,*, Enrique Muñoz1,2,†, and Marcelo Loewe3,4,‡

  • *Contact author: mimartinez1@uc.cl
  • †Contact author: ejmunozt@uc.cl
  • ‡Contact author: marcelo.loewe@uss.cl
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Phys. Rev. D 114, 096011 – Published 12 November, 2026

DOI: https://doi.org/10.1103/sfw1-csrl

Abstract

We consider a self-interacting charged scalar field represented by the complex λϕ4 model, embedded in a background electric field exhibiting classical stochastic fluctuations. We studied the effects of the classical stochastic noise on the physical parameters of the scalar field theory, for both weak and ultrastrong electric-field regimes. The stochastic background electric field is included in the Schwinger propagator through the covariant derivative, and the generating functional of the theory is found by means of the replica trick in order to compute the statistical average over electric fluctuations. As a result of the averaging process, an effective interaction between charged currents emerges, with a coupling constant proportional to the magnitude of the autocorrelation function of the electric-field fluctuations. We obtained the dressed propagators, the interaction vertices, and the renormalization group equations of the theory, along with the corresponding streamplots in the manifold of interaction couplings.

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Information

Phys. Rev. D 114, 096011– Published 12 November, 2026
  • Received 18 July 2026
  • Accepted 21 October 2026
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