Action Principle (Relativistic)

In classical mechanics, to fully describe a particle, one only needs to write down its Lagrangian: $$S=\int _a^b Ldt=\int _a^b T-U dt $$ $$=\int _a^b T dt +\int _a^b -U dt =S_P+S_{PF}$$ Here, the kinetic term \(T\) can be regarded as the Action \(S_P\) of a free particle, and the potential term \(U\) is the Action \(S_{PF}\) of the interaction between the particle and the field. In electromagnetism, we learn that the field also carries momentum and energy, so the complete description of electromagnetic motion includes the Action \(S_F\) of the field: $$S=S_P+S_{PF}+S_F$$

Originally written in Chinese by the author, these articles are translated into English to invite cross-language resonance.