Proca理论中的周期性电荷振荡
Periodic charge oscillations in the Proca theory
AI总结：
本文研究Proca理论中带电态的动力学，通过平均电场的振荡库仑分量和平均4-流解释周期性电荷振荡，并发现影响解析性的冲击波。
摘要：
我们考虑实质量矢量场的Proca理论。在这种理论中存在一个局域守恒的4-流算符，可以用它来定义电荷算符。因此，存在一些带电态，其中电荷算符的期望值非零。我们仔细考察了电荷算符，并研究了某一类带电态的动力学。为此，我们讨论了这些态中的平均电场和4-流。平均电场具有周期性振荡的库仑分量，该分量的存在解释了周期性电荷振荡。平均4-流为这种现象提供了互补的见解，对其讨论引出了某个悖论的识别。最后但同样重要的是，我们表明在所研究的系统中传播着一个冲击波，它影响平均电场和4-流的解析性。
英文摘要：
We consider the Proca theory of the real massive vector field. There is a locally conserved 4-current operator in such a theory, which one may use to define the charge operator. Accordingly, there are charged states in which the expectation value of the charge operator is non-zero. We take a close look at the charge operator and study the dynamics of the certain class of charged states. For this purpose, we discuss the mean electric field and 4-current in such states. The mean electric field has the periodically oscillating Coulomb component, whose presence explains the periodic charge oscillations. A complementary insight at such a phenomenon is provided by the mean 4-current, whose discussion leads to the identification of a certain paradox. Last but not least, we show that there is a shock wave propagating in the studied system, which affects analyticity of the mean electric field and 4-current.
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