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Ukr. J. Phys. 2015, Vol. 60, N 10, p.985-1006
doi:10.15407/ujpe60.10.0985    Paper

Simulik V.M.

Institute of Electron Physics, Nat. Acad. of Sci. of Ukraine
(21, Universytets’ka Str., Uzhgorod 88000, Ukraine; e-mail: vsimulik@gmail.com)

Derivation of the Dirac and Dirac-Like Equations of Arbitrary Spin from the Corresponding Relativistic Canonival Quantum Mechanics

Section: Fields and Elementary Particles
Original Author's Text: English

Abstract: The new relativistic equations of motion for the particles with spin s = 1, s = 3/2, and s = 2 and nonzero mass have been introduced. The description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. The manifestly covariant arbitrary-spin field equations that follow from the quantum mechanical equations have been considered. The covariant local field theory equations for a spin s = (1,1) particle-antiparticle doublet, spin s = (1,0,1,0) particle-antiparticle multiplet, spin s = (3/2,3/2) particle-antiparticle doublet, spin s = (2,2) particle-antiparticle doublet, spin s = (2,0,2,0) particle-antiparticle multiplet, and spin s = (2,1,2,1) particle-antiparticle multiplet have been introduced. The Maxwell-like equations for a boson with spin s = 1 and mass m > 0 have been introduced as well.

Key words: relativistic quantum mechanics, Schrödinger–Foldy equation, Dirac equation, Maxwell equations, arbitrary spin.