Cyclic structures of Cliffordian supergroups and particle representations of Spin_+(1,3)

CPT Groups of Spinor Fields in de Sitter and Anti-de Sitter Spaces

“…All other (finite-dimensional) representations of Spin + (1, 3), which compound higher spin fields, are derived by tensoring of spin-1/2 fields. There is a relationship between representations of Spin + (1, 3) and Clifford algebras [32,60]. At this point, complex representations of Spin + (1, 3) are described within a representation system M C = M 0 ⊕ M 1 , and real representations within a system M R = M + ⊕ M − , where 1)…”

“…Here the numbers l 0 and l 1 define a Gel'fand-Naimark representation basis of the Lorentz group (for more details see [32,60]). Hence it follows that the system M C = M 0 ⊕ M 1 and also the representations C l 0 3 and C l 0 7 of the block M − correspond to charged particles.…”

“…There are two classes of neutral particles: 1) particles which have antiparticles such as neutrons, neutrinos and so on; 2) particles which coincide with their antiparticles (for example, photons). The first class is described by the the algebras Cℓ p,q over the field F = R with the rings K ≃ H and K ≃ H ⊕ H (the types p − q ≡ 4, 6 (mod 8) and p − q ≡ 5 (mod 8)), and the second class (truly neutral particles) is described by the algebras Cℓ p,q over the field F = R with the rings K ≃ R and K ≃ R ⊕ R (the types p − q ≡ 0, 2 (mod 8) and p − q ≡ 1 (mod 8)) (for more details see [22,28,60]).…”

Spinor Structure and Internal Symmetries

“…There are two classes of neutral particles: 1) particles which have antiparticles such as neutrons, neutrinos and so on; 2) particles which coincide with their antiparticles (for example, photons). The first class is described by the the algebras Cℓ p,q over the field F = R with the rings K ≃ H and K ≃ H ⊕ H (the types p − q ≡ 4, 6 (mod 8) and p − q ≡ 5 (mod 8)), and the second class (truly neutral particles) is described by the algebras Cℓ p,q over the field F = R with the rings K ≃ R and K ≃ R ⊕ R (the types p − q ≡ 0, 2 (mod 8) and p − q ≡ 1 (mod 8)) (for more details see [37,38,41,42]).…”

Spinor Structure and Matter Spectrum

“…At this point, a level of the matter spectrum does not describe an elementary particle in its entirety, it describes only one state from the variety of all its possible states at the given value of energy. An elementary particle in itself is understood as a superposition of state vectors in nonseparable Hilbert space H S ⊗ H Q ⊗ H ∞ (for more details about structure of this space 2 see [12,13,14]). At the reduction of superposition one from the possible states (level of the matter spectrum) is realized in accordance with superselection rules and coherent subspaces of H S ⊗ H Q ⊗ H ∞ .…”