定义对电磁场所做的功
Defining work done on electromagnetic field
摘要：
定义通过运动电荷对电磁场（EMF）所做的功的问题没有现成的解决方案，因为EMF的标准哈密顿量不能预测规范不变的能量变化。这限制了统计力学在EMF中的应用。我们得到了一个新的，明确规范不变的哈密顿电磁场，只依赖于物理观测。这个哈密顿量允许定义对EMF所做的热力学功，并为所考虑的情况制定第二定律。这也导致了这个法律和电动时间箭头之间的直接联系，即选择延迟，而不是先进的解决方案的波动方程。测量热力学功可以给出光子质量是否很小但不为零的信息。
英文摘要：
The problem of defining work done on electromagnetic field (EMF) via moving charges does not have a ready solution, because the standard Hamiltonian of EMF does not predict gauge-invariant energy changes. This limits applications of statistical mechanics to EMF. We obtained a new, explicitly gauge-invariant Hamiltonian for EMF that depends only on physical observables. This Hamiltonian allows to define thermodynamic work done on EMF and to formulate the second law for the considered situation. It also leads to a direct link between this law and the electrodynamic arrow of time, i.e. choosing retarded, and not advanced solutions of wave-equations. Measuring the thermodynamic work can give information on whether the photon mass is small but non-zero.
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