Statistical Symmetry Breaking and Emergent Colored Noise in a Stochastic Scalar-Doublet Field Theory

Abstract

We investigate a relativistic stochastic field theory in which a complex scalar doublet is coupled to a complex white-noise source. The action preserves Lorentz and $\mathrm{U}(1)\times \mathrm{SU}(2)$ symmetries at the statistical level, whereas the corresponding Euler-Lagrange equations exhibit symmetry breaking along individual stochastic realizations. Within a gauge-field-free sector introduced to obtain analytical solutions, we show that the scalar doublet undergoes a noise-driven random walk in field space, leading to a finite, time-dependent ensemble average of its magnitude. As an illustrative application, we further investigate the coupling of the stochastic scalar field to fermions through a Yukawa interaction. The scalar-field solution naturally separates into a tail component, which contributes as an effective mass-like term, and a light-cone component, which acts as a colored-noise source that induces a spatially correlated stochastic phase in the fermion wave function. The statistical properties and correlation length of this emergent colored noise are derived analytically within the adopted approximations. The present work provides an exploratory study of statistical symmetry breaking and emergent colored-noise dynamics in a relativistic stochastic scalar-doublet field theory.

18 pages, 5 figures

References in corpus (10)

• Underground test of gravity-related wave function collapse
• Present status and future challenges of non-interferometric tests of collapse models
• Collapse models with non-white noises
• Testing the foundations of quantum physics in space Interferometric and non-interferometric tests with Large Particles
• Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom
• Collapse models with non-white noises II: particle-density coupled noises
• Progress in Higgs inflation
• Higgs-induced spectroscopic shifts near strong gravity sources
• Comparing geometric and gravitational particle production in Jordan and Einstein frames
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space