General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

Варламов, В. П.

doi:10.1007/s10773-006-9077-4

Cited by 15 publications

(44 citation statements)

References 46 publications

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“…From the Tab. 2 we see that 'admissible' hadron supermultiplets have degrees 1,8,10,27,28,35,55,64,80,81,91,125,136,143,154, . .…”

Section: Representations Of Su(3)mentioning

confidence: 97%

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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“…From the Tab. 2 we see that 'admissible' hadron supermultiplets have degrees 1,8,10,27,28,35,55,64,80,81,91,125,136,143,154, . .…”

Section: Representations Of Su(3)mentioning

confidence: 97%

Spinor Structure and Internal Symmetries

Варламов

2015

Int J Theor Phys

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“…The system of interlocking representations of the Lorentz group is shown on the Fig. 1 (for more details see [19,20]). Hence it follows that the each possible value of energy (energy level) is a vector state of the form (1):…”

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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“…do not satisfy the conditions of Clifford algebra, only the gs 2 dimensional representation is of help. The matrices for this irreducible representation are given in Equations (7), (8) and (9). We summarize the properties of the generalized Dirac group in detail in Table A1.…”

Section: Appendixmentioning

confidence: 99%

“…There is much formalism, which yields an adequate description of spin-s free particles, but when an electromagnetic field interaction is introduced, difficulties emerge. At present, there is no a fully adequate formalism for constructing relativistic wave equations for particles with arbitrary spin; all widely accepted higher spin formalisms have many intrinsic contradictions and difficulties ( [9] and references therein). In this study, a combined relativistic wave equation for the spin-s particles, where s ¼ 1/2, 3/2, 5/2, .…”

Section: Introductionmentioning

confidence: 99%

Dirac equation for particles with arbitrary half-integral spin

Guseinov

2011

Philosophical Magazine

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The sets of 2ð2s þ 1Þ-component irreducible and Clifford algebraic Hermitian and unitary matrices through the two-component Pauli matrices are suggested, where s ¼ 1/2, 3/2, 5/2, . . . . Using these matrix sets, the eigenvalues of which are AE1, the 2ð2s þ 1Þ-component generalized Dirac equation for a description of arbitrary half-integral spin particles is constructed. In accordance with the correspondence principle, the generalized Dirac equation suggested arises from the condition of relativistic invariance. This equation is reduced to the sets of two-component matrix equations the number of which is equal to 2s þ 1. The new relativistic invariant equation of motion leads to an equation of continuity with a positive-definite probability density and also to the Klein-Gordon equation. This relativistic equation is causal in the presence of an external electromagnetic field interaction. It is shown that, in the case of nonrelativistic limit, the relativistic equation presented is reduced to the Pauli equation describing the motion of half-integral spin particle in the electromagnetic field.

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General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

Cited by 15 publications

References 46 publications

Spinor Structure and Internal Symmetries

Spinor Structure and Internal Symmetries

Spinor Structure and Matter Spectrum

Dirac equation for particles with arbitrary half-integral spin

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