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.

arXiv comment18 pages, 5 figures

References in corpus (23)

• Higgs mass and vacuum stability in the Standard Model at NNLO
• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Underground test of gravity-related wave function collapse
• Upper bounds on spontaneous wave-function collapse models using millikelvin-cooled nanocantilevers
• Present status and future challenges of non-interferometric tests of collapse models
• Improved noninterferometric test of collapse models using ultracold cantilevers
• Room temperature test of the Continuous Spontaneous Localization model using a levitated micro-oscillator
• Collapse models with non-white noises
• Relativistic Collapse Model With Tachyonic Features
• Narrowing the parameter space of collapse models with ultracold layered force sensors
• An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse
• Testing Linearity of Quantum Theory with a Thermometer
• 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
• Atto-Nm Torque Sensing with a Macroscopic Optomechanical Torsion Pendulum
• Collapse models with non-white noises II: particle-density coupled noises
• Neutron star heating constraints on wave-function collapse models
• Progress in Higgs inflation
• Mass-coupled relativistic spontaneous collapse models
• Higgs-induced spectroscopic shifts near strong gravity sources
• On the (im)possibility of extending the GRW model to relativistic particles
• Comparing geometric and gravitational particle production in Jordan and Einstein frames
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space