General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics

Abstract

The investigation of arXiv 1409.2766v2 [quant-ph] has been continued by the general form of the numerous equations with partial values of arbitrary spin, which were considered in above mentioned preprint. The general forms of quantum-mechanical and covariant equations for arbitrary spin together with the general description of the arbitrary spin field formalism are presented. The corresponding relativistic quantum mechanics of arbitrary spin is given as the system of axioms. Previously ignored partial example of the spin s=(0,0) particle-antiparticle doublet is considered. The partial example of spin s=(3/2,3/2) particle-antiparticle doublet is highlighted. The new 64 dimensional Clifford--Dirac algebra over the field of real numbers is suggested. The general operator, which transformed the relativistic canonical quantum mechanics of arbitrary spin into the locally covariant field theory, has been introduced. Moreover, the study of the place of the results given in arXiv 1409.2766v2 [quant-ph] among the results of other authors is started. The review of the different investigations in the area of relativistic canonical quantum mechanics is given and the brief analysis of the existing approaches to the covariant field theory of arbitrary spin is initiated. The consideration of some important details of arXiv 1409.2766v2 [quant-ph] is improved.