Link between the relativistic canonical quantum mechanics of arbitrary spin and the corresponding field theory

23rd International Conference on Integrable Systems and Quantum Symmetries

Simulik, Volodimir^1

Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., Uzhgorod

88000, Ukraine^1

关键词: Arbitrary spin;    Covariant;    Covariant field equation;    Dirac equations;    Field theory;    Local field theories;    Quantum mechanical;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012047/pdf
DOI  :  10.1088/1742-6596/670/1/012047

来源: IOP

【 摘 要 】

The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass have been introduced. The axiomatic level description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The 64-dimensional ClR(0,6) algebra in terms of Dirac gamma matrices has been suggested. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equations for an arbitrary spin that follow from the quantum mechanical equations have been considered. The covariant local field theory equations for 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 the boson with spin s = 1 and nonzero mass have been introduced as well.