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摘要翻译：
引入了随机变形的概念，建立了相应的代数变形过程。这一过程类似于变形量化之类的可观测项代数的变形，但对于一个虚变形参数（普朗克常数）来说是如此。该方法在有限和无限自由度的相对论和非相对论模型上得到了证明。结果表明，在随机变形下，非相对论质点与弯曲背景上电磁场相互作用的模型转化为Fokker-Planck方程描述的随机模型，扩散张量为逆度量张量。对该系统的牛顿方程进行了第一次随机修正。还导出了Klein-Kramers方程作为某一经典模型的随机变形。将随机变形过程应用于适当的相对论经典模型，得到了Fokker-Planck和Klein-Kramers方程的相对论推广。本文还导出了与随机洛伦兹狄拉克方程相关联的福克-普朗克方程的模拟。研究了自由标量场和电磁场模型的随机变形。结果表明，在后一种情况下，所得到的随机模型描述了透明介质中的波动电磁场。
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英文标题：
《Fluctuations as stochastic deformation》
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作者：
P.O. Kazinski
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：High Energy Physics - Theory 高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
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PDF链接：
https://arxiv.org/pdf/711.3644
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