### Journals Information

**
Universal Journal of Physics and Application Vol. 11(6), pp. 202 - 234 DOI: 10.13189/ujpa.2017.110602 Reprint (PDF) (450Kb) **

## On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

**V.M. Simulik ^{*}**

Institute of Electron Physics, National Academy of Sciences, Uzhgorod, 88000, Ukraine

**ABSTRACT**

The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass, suggested by author in years 2014–2016, are under consideration. The complete version of brief paper in J. Phys: Conf. Ser., 670 (2016) 012047(1-16) is given. The axiomatic level description of the relativistic canonical quantum mechanics of an arbitrary mass and spin has been given. The 64-dimensional Cl^{R}(0,6) algebra in terms of Dirac gamma matrices has been suggested. The interpretation of the 28-dimensional gamma matrix representation of SO(8) algebra over the field of real numbers is given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory in the form of extended Foldy–Wouthuysen transformation has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equation for an arbitrary spin that follows from the corresponding equation of relativistic canonical quantum mechanics, has been considered. The found equations are without redundant components. The partial examples for spin s=3/2 and s=2 are presented. The covariant local field theory equations for spin s = (3/2,3/2) particle-antiparticle doublet and spin s = (2,2) particle-antiparticle doublet have been introduced. The Maxwell and slightly generalized Maxwell-like equations containing mass member have been considered as well.

**KEYWORDS**

Relativistic Quantum Mechanics, Quantum Field Theory, Relativistic Wave Equations, Higher Spin, Arbitrary Spin, Foldy–Wouthuysen Representation, Applied Clifford Algebras

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] V.M. Simulik , "On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin," Universal Journal of Physics and Application, Vol. 11, No. 6, pp. 202 - 234, 2017. DOI: 10.13189/ujpa.2017.110602.

(b). APA Format:

V.M. Simulik (2017). On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin. Universal Journal of Physics and Application, 11(6), 202 - 234. DOI: 10.13189/ujpa.2017.110602.