## New Equation of Motion of an Electron: the Covariance of Self-action

**Authors:** Xiaowen Tong

It is well known that our knowledge about the radiation reaction of an electron in classical electrodynamics is unambiguous, but the self-action is not. The latter corresponds to an electromagnetic mass which is not relativistically covariant. In this paper we first derive a new formula for energy density of electrostatic fields. By establishing a delay coordinate system, a classical equation of motion of an electron is then obtained based on the conservation of energy and momentum. Finally we calculate the self-energy of an electron in quantum electrodynamics and find that it merely leads to an additional mass of the electron. Thus the covariance of the self-action is proved without altering classical electrodynamics but with a direct cut-off imposed on the integral of the self-energy. The detail that the self-action becomes covariant in quantum electrodynamics is unknown. However, the interaction energy of an electron interacting with vacuum fluctuations can be easily calculated by assuming that every mode of the radiation fields is occupied by one real photon. Making use of all the results we obtain a semi-classical and covariant equation of motion of an electron.

**Comments:** Pages.

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### Submission history

[v1] 2018-12-20 05:42:31

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