Nonequilibrium dynamics of charged particles in a quantized electromagnetic field: causal, stable and self-consistent dynamics from 1/c expansion

作者：Fleming C H^*; Johnson P R; Hu B L

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(25): 255002.

DOI：10.1088/1751-8113/45/25/255002

We derive a set of stochastic equations of motion for a system of ordinary quantum-mechanical, spinless charged particles in a second-quantized electromagnetic field based on a consistent application of a dimensionful 1/c expansion, which is analogous to the post-Newtonian expansion in gravity. All relativistic corrections up to order 1/c(3) are found, including electrostatic interactions (Coulomb), magnetostatic backreaction (Biot-Savart), dissipative backreaction (Abraham-Lorentz) and quantum-field fluctuations at zero and finite temperatures. With self-consistent backreaction of the EM field included, we show that this approach yields causal and runaway-free equations of motion, provides new insights into charged-particle backreaction and naturally leads to equations consistent with the (classical) Darwin Hamiltonian, and has quantum operator ordering consistent with the Breit Hamiltonian. To order 1/c(3) the approach leads to a nonstandard mass renormalization which is associated with magnetostatic self-interactions, and no cutoff is required to prevent runaways. Our results also show that the pathologies of the standard Abraham-Lorentz equations can be seen as a consequence of applying an inconsistent (i.e. incomplete, mixed-order) expansion in 1/c, if, from the start, the analysis is viewed as generating an effective theory with all relativistic corrections considered perturbatively. Finally, we show that the 1/c expansion within a Hamiltonian framework yields well-behaved noise and dissipation, in addition to the multiple-particle interactions.

• 出版日期2012-6-29