Relativistic wave equations of arbitrary spin in quantum mechanics and field theory, example spin s=2

Abstract

Relativistic wave equations for the particles of arbitrary spin suggested by Bhabha, Bargmann–Wigner, Rarita–Schwinger (for spin s = 3/2) and other authors are under consideration. The comparison with the equations introduced recently by the author in Ukr. J. Phys., Vol. 60, N 10. 985–1006 (2015) and J. Phys.; Conf. Ser. Vol. 670, 012047(1–16) (2016) is given. The advantages of the new equations are considered brie y. The three level consideration (relativistic canonical quantum mechanics, canonical Foldy–Wouthuysen type field theory, locally covariant field theory) is presented. The operator link between the relativistic canonical quantum mechanics and locally covariant field theory of arbitrary spin is found. This link is given by the extended Foldy–Wouthuysen transwormation between the 2(2s+1)- component local field theory and the corresponding relativistic canonical quantum mechanics. The important partial example of spin s=2 case is considered in details. The 10-component Dirac-like wave equation for the spin s=(2,2) particle-antiparticle doublet is suggested. The link with 10-component Maxwell-like equation for this doublet is considered brifly. The hypothesis on the spin s=5/2 particle is discussed.