Spinor Structure and Internal Symmetries

Abstract

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries $P$, $T$ and their combination $PT$ are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation $C$ is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation $C$ allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and $SU(3)$-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of $SU(3)$). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of $SU(3)$-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann--Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

44 pages

References in corpus (5)

• Group Averaging for de Sitter free fields
• Field on Poincare group and quantum description of orientable objects
• Spherical functions on the de Sitter group
• Group Theoretical Interpretation of the CPT-theorem
• The CPT Group in the de Sitter Space

Cited by in corpus (9)

• Majorana states for subluminal structured photons
• Spinor Structure and Matter Spectrum
• Lorentz group and mass spectrum of elementary particles
• Conformal numbers
• Holographic coordinates
• Spinor Structure and Modulo 8 Periodicity
• On the group theoretical approach to relativistic wave equations for arbitrary spin
• On algebraic structure of matter spectrum
• Group Theoretical Description of Mendeleev Periodic System