A modification of electrodynamics is proposed, motivated by previously unremarked paradoxes that can occur in the standard formulation. It is shown by specific examples that gauge transformations exist that radically alter the nature of a problem, even while maintaining the values of many measurable quantities. In one example, a system with energy conservation is transformed to a system where energy is not conserved. The second example possesses a ponderomotive potential in one gauge, but this important measurable quantity does not appear in the gauge-transformed system. A resolution of the paradoxes comes from noting that the change in total action arising from the interaction term in the Lagrangian density cannot always be neglected, contrary to the usual assumption. The problem arises from the information lost by employing an adiabatic cutoff of the field. This is not necessary. Its replacement by a requirement that the total action should not change with a gauge transformation amounts to a supplementary condition for gauge invariance that can be employed to preserve the physical character of the problem. It is shown that the adiabatic cutoff procedure can also be eliminated in the construction of quantum transition amplitudes, thus retaining consistency between the way in which asymptotic conditions are applied in electrodynamics and in quantum mechanics. The ‘gauge-invariant electrodynamics’ of Schwinger is shown to depend on an ansatz equivalent to the condition found here for maintenance of the ponderomotive potential in a gauge transformation. Among the altered viewpoints required by the modified electrodynamics, in addition to the rejection of the adiabatic cutoff, is the recognition that the electric and magnetic fields do not completely determine a physical problem, and that the electromagnetic potentials supply additional information that is required for completeness of electrodynamics.

中文翻译：

---

关于修正的电动力学

提出了对电动力学的修改，其动机是先前未注意到的悖论可能出现在标准公式中。具体例子表明，存在规范转换，从根本上改变了问题的性质，即使在保持许多可测量量的值时也是如此。在一个例子中，一个能量守恒的系统被转换成一个能量不守恒的系统。第二个例子在一个规范中具有质动力势，但这个重要的可测量量并没有出现在规范转换系统中。悖论的解决来自于注意到拉格朗日密度中相互作用项引起的总作用的变化不能总是被忽略，这与通常的假设相反。问题是由于采用场的绝热截止导致信息丢失。这是没有必要的。它被总作用不应随规范变换改变的要求所替代，相当于规范不变性的补充条件，可用于保持问题的物理特征。结果表明，在构造量子跃迁幅度时也可以消除绝热截止过程，从而保持渐近条件在电动力学和量子力学中的应用方式之间的一致性。Schwinger 的“规范不变电动力学”被证明依赖于一个 ansatz 等效于这里发现的条件，用于维持规范变换中的有质动力势。