arXiv subjects

N. A. Gromov

Publications and source records attributed to N. A. Gromov.

At least 19 recordsLinked to original sources

arXiv2022

The contraction hypothesis of the gauge group of the Standard Model and LHC experimental data

Within the framework of the contraction hypothesis of the gauge group of the Standard Model the behavior of the amplitude of the dominant Higgs boson production process in the four-lepton decay with increasing temperature $T$ is analyzed. It is shown that the modified process breaks down into a number of channels depending on the contribution of the color components in the loop of virtual quarks, leading to the creation of the Higgs boson. The dependence on $T$ of the cross section of each channel is found. Comparison with LHC data on Higgs boson creation cross sections at energies (temperatures) of 7, 8, 13, and 14 TeV showed that the hypothesis about the contraction of the gauge group of the Standard Model does not contradict these data.

physics.gen-ph↗

arXiv2021

Higher-Energy Standard Model from the Gauge Group Contraction

The evolution of properties and interactions of elementary particles is described, beginning with the Planck scale of $10^{19}$ GeV. The description is based on the hypothesis that high-temperature (high-energy) limit of the Standard Model is generated by the gauge group contraction. In the infinite-temperature limit, properties of particles fundamentally change: all particles lose their masses, only massless neutral $Z$ bosons and $u$ quarks together with neutrinos and photons survive. Weak interactions become long-range ones and are generated by neutral currents. Quarks have only one color degree of freedom.

hep-ph↗

arXiv2020

Nonrelativistic quantum particles on the Minkowski plane

The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schrödinger equations for eigenvalues are obtained using the Beltrami-Laplas operator of the pseudo-Euclidean plane and the corresponding potentials. It is shown that, in contrast to the standard problem on Euclidean plane, in addition to the continuous spectrum, a free particle has a discrete energy levels and a Coulomb particle, in addition to the discrete spectrum, has unstable states that describe the incidence of a particle on isotropic lines forming a metric cone.

quant-ph↗

arXiv2015

Integrable potentials on Cayley-Klein spaces from quantum groups

The family of (super)integrable potentials on spaces with curvature developed by A. Ballesteros et all is extend to all two-dimensional Cayley-Klein spaces with the help of contractions. It is shown that integrable systems on spaces with degenerate metrics are described by two Hamiltonians: one in the base and another in the fiber.

math-ph↗

arXiv2010

Noncommutative quantum analogs of constant curvature spaces

The quantum N-dimensional orthogonal vector Cayley-Klein spaces with different combinations of quantum structure and Cayley-Klein scheme of contractions and analytical continuations are described for multipliers, which include the first and the second powers of contraction parameters in the transformation of deformation parameter. The noncommutative analogs of constant curvature spaces are introduced. The low dimensional spaces with N=3,4 are discussed in detail and all quantum analogs of the fibered spaces corresponding to nilpotent values of contraction parameters are given. As a result the wide variety of the quantum deformations are obtained.

math-ph↗

arXiv2010

Higgsless Electroweak Model and Contraction of Gauge Group

A modified formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The {\it free} Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same experimentally verified fields with the same masses as the Standard Electroweak Model. The vector bosons masses are automatically generated, so there is no need in special mechanism of spontaneous symmetry breaking. The limiting case of the modified Higgsless Electroweak Model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson, electromagnetic and electron fields are interpreted as an external ones with respect to W-bosons and neutrino fields. The W-bosons and neutrino fields do not effect on these external fields. The masses of all particles remain the same, but the field interactions in contracted model are more simple as compared with the standard Electroweak Model due to nullification of some terms.

math-ph↗

arXiv2010

Possible quantum kinematics. II. Non-minimal case

The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction parameters in the transformation of deformation parameter. The noncommutative analogs of (N-1)-dimensional constant curvature spaces are introduced. Part of these spaces for N=5 are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the wide variety of the quantum deformations of realistic kinematics are suggested.

math-ph↗

arXiv2008

Analog of Electroweak Model for Contracted Gauge Group

The limiting case of the bosonic part of the standard Electroweak Model, which correspond to the contracted gauge group $ SU(2;j)\times U(1)$ is discussed. The Higgs boson, Z-boson and electromagnetic fields become an external ones with respect to the W-bosons fields. The W-bosons fields do not effect on these external fields. The masses of the all particles of the Electroweak Model remain the same under contraction.

math-ph↗

arXiv2008

The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple fibered semi-Riemannian geometry is the most appropriate one for the treatment of more then three different physical quantities as unified geometrical field theory. Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional fiber $x^5,$ responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise. PACS: 04.50.Cd, 02.40.-k, 11.10.Kk

gr-qc↗

arXiv2007

Higgsless Electroweak Theory following from the Spherical Geometry

A new formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The free Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same fields with the same masses as the Standard Electroweak Model. The vector bosons and electron masses are generated automatically, so there is no need in special mechanism.

hep-th↗

arXiv2006

Gauge Theories with Cayley-Klein $SO(2;j)$ and $SO(3;j)$ Gauge Groups

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.

hep-th↗

arXiv2006

Gauge Theories for Target Spaces with Degenerate Metrics

Some gauge theories for fiber target spaces with degenerate metrics are regarded. The gauge theory with Galilei group G(2) is obtained as a contraction of SO(2) gauge theory with Higgs mechanism. The analogue of the standard electroweak theory for contracted SU(2) group is considered. It is shown that the gauge field theory with degenerate metrics in target (matter) field space describe the same set of fields and particle mass as initial one, if Lagrangians in the base and in the fiber both are taken into account. Such theory based on non-semisimple contracted group provide more simple field interactions as compared with initial one. The conjecture is advanced that Higgs boson being an artefact of the Higgs mechanism is unobservable.

hep-th↗

arXiv2006

Linear harmonic oscillator in spaces with degenerate metrics

With the help of contraction method we study the harmonic oscillator in spaces with degenerate metrics, namely, on Galilei plane and in the flat 3D Cayley-Klein spaces $R_3(j_2,j_3).$ It is shown that the inner degrees of freedom are appeared which physical dimensions are different from the dimension of the space.

math-ph↗

arXiv2005

Noncommutative space-time models

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N=5 part of them are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.

hep-th↗

arXiv2004

Quantum kinematics

The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of $(N-1)$-dimensional constant curvature spaces are introduced. Part of the 4-dimensional constant curvature spaces are interpreted as the non-commutative analogs of $(1+3)$ kinematics. A different unifications of Cayley-Klein and Hopf structures in a kinematics are described with the help of permutations. All permutations which lead to the physically nonequivalent kinematics are found and the corresponding non-commutative $(1+3)$ kinematics are investigated. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length, the fundamental mass and the fundamental velocity are obtained.

hep-th↗

arXiv2004

Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups

Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $ GL_q(1|2)$ and corresponding quantum superspace $ C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $ C_h(1|2;ι)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.

math.QA↗

arXiv2004

Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis

Spaces of constant curvature and their motion groups are described most naturally in Cartesian basis. All these motion groups also known as CK groups are obtained from orthogonal group by contractions and analytical continuations. On the other hand quantum deformation of orthogonal group $SO(N) $ is most easily performed in so-called symplectic basis. We reformulate its standard quantum deformation to Cartesian basis and obtain all possible contractions of quantum orthogonal group $SO_q(N)$ both for untouched and transformed deformation parameter. It turned out, that similar to undeformed case all CK contractions of $SO_q(N)$ are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of $SO_q(N), N=3,4,5$ are regarded as an examples.

math.QA↗

arXiv2003

Induced Representations of Cayley-Klein Orthogonal Groups

Using method of inducing, irreducible unitary representation of Cayley--Klein orthogonal groups were constructed. There was proved that Kirilov's method of orbits is relevant for study of the behavior of irreducible representations under transitions between Cayley--Klein groups.

math-ph↗