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

Варламов, В. П.

doi:10.1007/s00006-014-0487-8

Cited by 12 publications

(12 citation statements)

References 60 publications

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“…Note that ǫ and ǫ ′′ are the same functions of n as κ and κ ′′ are of m. These signs were defined so that ǫ and ǫ ′′ agree with Connes' KO-dimension tables [5,17]. Related tables can be found in the literature [18][19][20]. The values of the KO dimension n and of the new dimension m in terms of the conventions are given in Table 2.…”

Section: Automorphisms Of Clifford Algebrasmentioning

confidence: 99%

Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics

Brouder

Besnard²

2018

Journal of Mathematical Physics

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An analogy with real Clifford algebras on even-dimensional vector spaces suggests to assign a couple of space and time dimensions modulo 8 to any algebra (represented over a complex Hilbert space) containing two self-adjoint involutions and an anti-unitary operator with specific commutation relations.It is shown that this assignment is compatible with the tensor product: the space and time dimensions of the tensor product are the sums of the space and time dimensions of its factors. This could provide an interpretation of the presence of such algebras in P T -symmetric Hamiltonians or the description of topological matter.This construction is used to build an indefinite (i.e. pseudo-Riemannian) version of the spectral triples of noncommutative geometry, defined over Krein spaces instead of Hilbert spaces. Within this framework, we can express the Lagrangian (both bosonic and fermionic) of a Lorentzian almost-commutative spectral triple. We exhibit a space of physical states that solves the fermion-doubling problem. The example of quantum electrodynamics is described.

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Section: Automorphisms Of Clifford Algebrasmentioning

confidence: 99%

Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics

Brouder

Besnard²

2018

Journal of Mathematical Physics

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“…In our case, pure states of the form (3) correspond to charged states. At this point, the sign of charge is changed under action of the pseudoautomorphism A → A of the complex spinor structure (for more details see [24,25,26]). Following to analogy with the Lagrangian formalism, where neutral particles are described by real fields, we introduce vector states of the form…”

Section: Concrete Realization π(A)mentioning

confidence: 99%

“…States of the form (4) correspond to neutral states. Since the real spinor structure is appeared in the result of reduction C 2(k+r) → Cℓ p,q , then (as a consequence) a charge conjugation C (pseudoautomorphism A → A) for the algebras Cℓ p,q over the real number field F = R and quaternionic division ring K ≃ H (the types p − q ≡ 4, 6 (mod 8)) is reduced to particle-antiparticle interchange C ′ (see [24,25,26]). As is known, there exist two classes of neutral particles: 1) particles which have antiparticles, such as neutrons, neutrino 4 and so on; 2) particles which coincide with their antiparticles (for example, photons, π 0 -mesons and so on), that is, so-called truly neutral particles.…”

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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“…The relationship between CP T groups and extraspecial groups and universal coverings of orthogonal groups was established in [37,38]. 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%

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

Cited by 12 publications

References 60 publications

Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics

Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics

Spinor Structure and Matter Spectrum

Spinor Structure and Internal Symmetries

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