经典辐射反应对协变洛伦兹力的离壳修正
Classical Radiation Reaction Off-Shell Corrections to the Covariant Lorentz Force
摘要：
Gupta和Padmanabhan已经证明，Abraham-Lorentz-Dirac方程的辐射反作用力可以通过从加速带电粒子的惯性系到实验室的惯性系的坐标变换来获得。我们证明了这个问题可以在一个五维平坦空间中表述，在经典的Stueckelberg-Feynman-Schwinger协变力学的完全规范协变形式的框架中有五个相应的规范场（0，1，2，3分量的零模场对应于Maxwell场）.如果没有额外的约束，粒子和场就不局限于它们的质量壳。我们表明，在质量壳极限，广义洛伦兹力通过延迟格林函数的五维场方程提供了经典的Abraham-Lorentz-Dirac辐射反应项（重正化质量和电荷）。我们还得到了一般的耦合方程的轨道和离壳动力学质量的演变过程中。如果粒子在壳层上保持不变，这个理论就不承认辐射。方程的结构意味着当外场被去除时，质量壳偏差是有界的。
英文摘要：
It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham-Lorentz-Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg- Feynman-Schwinger covariant mechanics (the zero mode fields of the 0,1,2,3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five-dimensional field equations provides the classical Abraham-Lorentz-Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution. The theory does not admit radiation if the particle remains identically on-shell. The structure of the equations implies that the mass-shell deviaiton is bounded when the external field is removed.
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