Connection between the energy-momentum vector and the canonical momentum in relativistic mechanics

Yu. A. Rylov


Abstract: Relativistic mechanics is regarded as a limiting case of a mechanics with four independent canonical momenta $p_i$. It is shown that creation and annihilation of particles is possible in this limiting case. A connection is established between the energy-momentum vector of a particle and its canonical momentum. The usual relation $E=-p_0$ between the energy of a particle and the time component of the canonical momentum is a special case and is only valid when the world line of the particle does not double back in time.

Received: 28.04.1969

 English version: Theoretical and Mathematical Physics, 1970, 2:3, 240–243