发表机构
Department of Physics, Zhejiang Normal University（浙江师范大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探索相对论性随机标量二重态场论的统计对称性破缺，解析推导其涌现色噪声的统计性质与关联长度，为相关动力学研究提供了探索性基础。
AI 中文摘要
我们研究一种相对论性随机场论，其中复标量二重态与复白噪声源耦合。该作用量在统计层面保持洛伦兹对称性和U(1)×SU(2)对称性，而对应的欧拉-拉格朗日方程在单个随机实现中呈现对称性破缺。为获得解析解，我们引入无规范场的子领域，结果表明标量二重态在参数空间中发生由噪声驱动的随机游走，导致其模的系综平均为有限值且随时间变化。作为示例应用，我们进一步研究该随机标量场通过汤川相互作用与费米子的耦合。标量场解自然分为尾部分量（作为类有效质量项贡献）和光锥分量（作为色噪声源，在费米子波函数中诱导空间关联的随机相位）。在采用的近似下，我们解析推导了该涌现色噪声的统计性质和关联长度。本工作是对相对论性随机标量二重态场论中统计对称性破缺与涌现色噪声动力学的探索性研究。
英文摘要
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.
Comments18 pages, 5 figures
Journal refPhys. Scr. 101, 315203 (2026)
