相对论粒子在量子场中运动的随机理论：II。标量Abraham-Lorentz-Dirac-Langevin方程、辐射反应和真空涨落
Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
摘要：
本文应用开放系统的概念和影响泛函理论建立了量子标量场中相对论运动无自旋粒子的随机理论。介于量子和半经典之间的随机机制抓住了完整理论的统计力学属性。将粒子中心世界线量子化公式应用于标量QED的量子场论，导出了含时（标量）Abraham-Lorentz-Dirac（ALD）方程，并证明了它是非线性粒子场系统的正确的半经典极限，而不需要作偶极或非相对论近似.进展到随机制度，我们推导出非线性耦合粒子场系统的多粒子ALD-Langevin方程。这些方程，我们展示了如何解决依赖于时间的耗散/噪声/重整化的半经典和随机限制的QED。阐明了辐射反应、量子耗散和真空涨落的关系以及初始条件在产生非洛仑兹不变噪声中的作用。我们强调退相干在达到半经典极限中的基本作用，这也表明了正确的方式来思考失控的解决方案和预加速的问题，从ALD方程中的三阶导数项的存在。我们表明，以这种方式获得的半经典自洽的解决方案是“悖论”和病理免费技术和概念。这种自洽的处理作为一个新的平台，调查有关的相对论运动电荷的问题。
英文摘要：
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semi-classical captures the statistical mechanical attributes of the full theory. Applying the particle-centric world-line quantization formulation to the quantum field theory of scalar QED we derive a time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or non-relativistic approximations. Progressing to the stochastic regime, we derive multiparticle ALD-Langevin equations for nonlinearly coupled particle-field systems. With these equations we show how to address time-dependent dissipation/noise/renormalization in the semiclassical and stochastic limits of QED. We clarify the the relation of radiation reaction, quantum dissipation and vacuum fluctuations and the role that initial conditions may play in producing non-Lorentz invariant noise. We emphasize the fundamental role of decoherence in reaching the semiclassical limit, which also suggests the correct way to think about the issues of runaway solutions and preacceleration from the presence of third derivative terms in the ALD equation. We show that the semiclassical self-consistent solutions obtained in this way are ``paradox'' and pathology free both technically and conceptually. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.
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