Geodesic
Connection between the energy-momentum vector and the canonical momentum in relativistic mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 333-337 
Yu. A. Rylov. Connection between the energy-momentum vector and the canonical momentum in relativistic mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 333-337. http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a6/
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     author = {Yu. A. Rylov},
     title = {Connection between the energy-momentum vector and the canonical momentum in relativistic mechanics},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. A. Fok, Izv. AN SSSR, OMEN, 1937, 551 ; В. А. Фок, Работы по квантовой теории поля, Сб., Изд-во Ленинградского ун-та, 1957

[2] L. D. Landau, E. M. Lifshits, Teoriya polya, Fizmatgiz, 1962 | MR

[3] S. Shveber, Vvedenie v relyativistskuyu kvantovuyu teoriyu polya, IL, 1963

[4] E. C. G. Stueckelberg, Helv. Phys. Acta, 15 (1942), 23 | MR | Zbl

[5] R. P. Feynman, Phys. Rev., 76 (1949), 749 ; Noveishee razvitie kvantovoi elektrodinamiki, Sb., IL, 1957 | DOI | MR | Zbl