CPT Groups of Higher Spin Fields

Варламов, В. П.

doi:10.1007/s10773-011-1022-5

Cited by 15 publications

(19 citation statements)

References 48 publications

(85 reference statements)

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“…Subsequent 'clothing' of the operator algebra leads to introduction of new properties (characteristics) of the state. For example, discrete symmetries (space inversion P , time reversal T , charge conjugation C and their combinations) are appeared as automorphisms of spinor structure associated with the each state of the form (2)-(4) [27,28,29,30] (see also recent paper on spinors transformations [31]). Further, a fractal structure of matter spectrum (third layer of 'clothing') is defined by the Cartan-Bott periodicity of spinor structure [32].…”

Section: Concrete Realization π(A)mentioning

confidence: 99%

Spinor Structure and Matter Spectrum

Варламов

2016

Int J Theor Phys

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Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations). All these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type $(l,0)\oplus(0,l)$, where $l$ is a spin value, whereas for arbitrary spin chains we have degenerate spectrum. Energy spectra of the stability levels (electron and proton states) of the matter spectrum are studied in detail. It is shown that these stability levels have a nature of threshold scales of the fractal structure associated with the system of interlocking representations of the Lorentz group.Comment: 36 page

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Section: Concrete Realization π(A)mentioning

confidence: 99%

Spinor Structure and Matter Spectrum

Варламов

2016

Int J Theor Phys

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“…We claim that any irreducible finite dimensional representation τ ll of the group SL(2, C) corresponds to a particle of the spin s, where s = |l −l| (see also [13]…”

Section: Definition Of the Spinmentioning

confidence: 99%

“…CP T groups of spinor fields in the de Sitter spaces of different signatures were studied in the works [39,40,41]. CP T groups for higher spin fields have been defined in [13] on the spinspaces associated with representations of the spinor group Spin + (1, 3).…”

Section: Cp T Groupmentioning

confidence: 99%

“…Charge multiplets, considered above, compound eight-dimensional regular representation of SU(3) 13 . 13 At this point we do not use the quark structure of F 1/2 , since this structure is a derivative construction of 5.2 Octet B 0 B 0 is a bosonic supermultiplet of SU(3) containing mesons of the spin 0 with the negative parity P 2 = −1. Hence it follows that all the particles of B 0 are described by the vectors of the abstract Hilbert space belonging to spin-0 line.…”

Section: 1mentioning

confidence: 99%

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Spinor Structure and Internal Symmetries

Варламов

2015

Int J Theor Phys

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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 Poincar\'{e} 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.Comment: 44 page

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“…Varlamov [4], where the author proposes a general method for the construction of CPT groups for fields of any spin. In this work, the cases of spin-1/2 and spin-3/2 are included, among others.…”

Section: Matrix and Operator Cpt Groupsmentioning

confidence: 99%