International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

Angular symmetry of space-time and the spinor representation of Poincaré group

R. A. Sventkovsky
  • R. A. Sventkovsky
  • Technical Sciences, CITiS, Presnenskii val str., 19, Moscow 123557, Russia
  • Google Scholar


  •  Received: 11 December 2013
  •  Accepted: 24 February 2014
  •  Published: 16 May 2014

Abstract

In the paper, a relativistic theory is suggested; we add three independent angles to the four coordinates of the Minkowski space that define the (x, t) - position of a moving local observer. These angular coordinates define the orientation of an observer under free rotations and they allow us to introduce the generators of the Poincaré group in the angular representation. Instead of a multi-component wave function of any spin-component wave function, one component wave function Y (and its Lorentz transform) is introduced, depending on the four coordinates of Minkowski space and three angular coordinates. Poincaré invariant first-order linear differential equations are derived. The matrix representation of the above operator equations based on appropriate angular is equivalent to Dirac and Maxwell equations. It is predicted and proven that the number of generations of leptons is three.
 
Key words: Spinor representation, generators of the Poincaré group, dimensions of Minkowski space.