arXiv subjects

B. M. Barbashov

Publications and source records attributed to B. M. Barbashov.

At least 19 recordsLinked to original sources

arXiv2013

Conformal and Affine Hamiltonian Dynamics of General Relativity

The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum energy of physical fields provides a good description of the type Ia supernova luminosity distance--redshift relation. Introducing the uncertainty principle at the Planck's epoch within our model, we obtain the hierarchy of the Universe energy scales, which is supported by the observational data. We found that the invariance of the Maurer-Cartan forms with respect to the general coordinate transformation yields a single-component strong gravitational waves. The Hamiltonian dynamics of the model describes the effect of an intensive vacuum creation of gravitons and the minimal coupling scalar (Higgs) bosons in the Early Universe.

gr-qc↗

arXiv2010

Conformal Hamiltonian Dynamics of General Relativity

The General Relativity formulated with the aid of the spin connection coefficients is considered in the finite space geometry of similarity with the Dirac scalar dilaton. We show that the redshift evolution of the General Relativity describes the vacuum creation of the matter in the empty Universe at the electroweak epoch and the dilaton vacuum energy plays a role of the dark energy.

gr-qc↗

arXiv2009

Is it possible to estimate the Higgs Mass from the CMB Power Spectrum?

General Relativity and Standard Model are considered as a theory of dynamical scale symmetry with definite initial data compatible with the accepted Higgs mechanism. In this theory the Early Universe behaves like a factory of electroweak bosons and Higgs scalars, and it gives a possibility to identify three peaks in the Cosmic Microwave Background power spectrum with the contributions of photonic decays and annihilation processes of primordial Higgs, W, and Z bosons in agreement with the QED coupling constant, Weinberg's angle, and Higgs' particle mass of about 118 GeV.

hep-ph↗

arXiv2007

Higgs effect in Conformal Cosmology & Supernova Data

The formulation of the Higgs effect is studied in the Glashow--Weinberg--Salam Standard Model, where the constant part of the Higgs potential is identified with the zeroth mode of the Higgs field. In this model, the Coleman--Weinberg effective potential obtained from the vacuum--vacuum transition amplitude is equal to unity at the extremum. This extremum immediately removes tremendous vacuum cosmological density and predicts mass of Higgs field. In this model, the kinetic energy density of the Higgs field and any scalar field can be treated as the rigid state origin that explains Supernova data in the conformal cosmology without the $Λ$ term.

hep-ph↗

arXiv2007

On Hamiltonian Approach to Standard Model

The vector bosons models including Standard Model (SM) are investigated in the framework of the Dirac Hamiltonian method with explicit resolving the Gauss constraints in order to eliminate variables with zero momenta and negative energy contributions in accordance with the operator quantization principles. The Hamiltonian formulation admits the dynamic version of the Higgs potential, where its constant parameter is replaced by the dynamic zero Fourier harmonic of the very Higgs field. In this case, the zero mode equation is a new sum-rule that predicts mass of Higgs field $m_h=\sqrt{6m^2_t-4[2M_W^2+M_Z^2]}=311.6\pm 8.9 {\rm GeV}$. The Hamiltonian formulation leads to static interactions playing the crucial role in the off-mass-shell phenomena of the type of bound state and a kaon - pion transition in the weak nonleptonic decays.

hep-th↗

arXiv2006

Hamiltonian General Relativity in CMB frame

A collection of requirements to the General Relativity that follow from the WMAP observations of the Cosmic Microwave Background radiation anisotropy as an inertial frame are discussed. These obligations include the separation of both the CMB frame from the diffeomorphisms and the diffeo-invariant cosmic evolution from the local scalar metric component in the manner compatible with the canonical Hamiltonian approach to the Einstein--Hilbert theory with the energy constraints. The solution of these constraints in classical and quantum theories and a fit of units of measurements are discussed in the light of the last Supernovae data.

gr-qc↗

arXiv2006

The Hamiltonian approach to General Relativity and CMB primordial spectrum

Approaches to solutions of problems of the energy, time, Hamiltonian operator quantization of the General Relativity, the creation of the Universe from vacuum are considered in the frame of reference associated with the CMB radiation in order to describe parameters of this radiation in terms of the parameters of the Standard Model of elementary particles.

hep-th↗

arXiv2006

Solution of Constraints in Theory of Relativistic String

The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Noether theorem. This coincidence allows us to solve the energy constraint, and fulfil Dirac's Hamiltonian reduction.

hep-th↗

arXiv2005

Hamiltonian Cosmological Perturbation Theory

The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification preserves the number of variables and leads to a cosmological perturbation theory with the scalar potential perturbations in contrast to the kinetic perturbations in the Lifshitz version which are responsible for the ``primordial power spectrum'' of CMB in the inflationary model. The Hamiltonian approach enables to explain this ``spectrum'' in terms of scale-invariant variables and to consider other topical problem of modern cosmology in the context of quantum cosmological creation of both universes and particles from the stable Bogoliubov vacuum.

hep-th↗

arXiv2005

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

The Hamiltonian formulation of general relativity (GR) is considered in finite space-time and a specific frame of reference given by the diffeo-invariant components of the Fock simplex in terms of the Dirac -- ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to the generalization of the Schwarzschild solution. The astrophysical application of this approach to GR is considered under supposition that the Dirac -- ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

astro-ph↗

arXiv2005

Quantum Gravity as Theory of "Superfluidity"

A version of the cosmological perturbation theory in general relativity (GR) is developed, where the cosmological scale factor is identified with spatial averaging of the metric determinant logarithm and the cosmic evolution acquires the pattern of a superfluid motion: the absence of "friction-type" interaction, the London-type wave function, and the Bogoliubov condensation of quantum universes. This identification keeps the number of variables of GR and leads to a new type of potential perturbations. A set of arguments is given in favor of that this "superfluid" version of GR is in agreement with the observational data.

gr-qc↗

arXiv2005

CMBR anisotropy: theoretical approaches

The version of the cosmological perturbation theory based on exact resolution of energy constraint is developed in accordance with the diffeomorphisms of general relativity in the Dirac Hamiltonian approach. Such exact resolution gives one a possibility to fulfil the Hamiltonian reduction and to explain the ``CMBR primordial power spectrum'' and other topical problems of modern cosmology by quantization of the energy constraint and quantum cosmological origin of matter.

astro-ph↗

arXiv2004

Hamiltonian Cosmological Dynamics of General Relativity

The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an evolution generator in the field space of events with the postulate about a physical vacuum as a state with the minimal eigenvalue of this generator. The cosmological scale factor is extracted from the Hamiltonian General Relativity without double counting of the spatial metric determinant in contrast to the standard cosmological perturbation theory. The Friedmann-like equations in the exact theory are derived. A new version of cosmological perturbation theory keeps the form of the Newton interactions in an early Universe. We show how the considered Hamiltonian approach to GR can solve the topical problems of modern cosmology and quantum theory of gravitation. cosmology and quantum theory of gravitation.

astro-ph↗

arXiv2001

On the Canonical Treatment of Lagrangian Constraints

The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a special Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge,

hep-th↗

arXiv2001

Time reparametrization-invariant dynamics of a relativistic string

The time-reparametrization-invariant dynamics of a relativistic string is studied in the Dirac generalized Hamiltonian theory by resolving the first class constraints. The reparametrization-invariant evolution parameter is identified with the time-like coordinate of the "center of mass" of a string which is separated from local degrees of freedom by transformations conserving the group of diffeomorphisms of the generalized Hamiltonian formulation and the Poincare covariance of local constraints. To identify the "center of mass" time-like coordinate with the invariant proper time (measured by an observer in the comoving frame of reference), we apply the Levi-Civita - Shanmugadhasan canonical transformations which convert the global (mass-shell) constraint into a new momentum, so that the corresponding gauge is not needed for the Hamiltonian reduction. The resolving of local constraints leads to an "equivalent unconstrained system" in the reduced phase space with the Roehrlich-type Hamiltonian of evolution with respect to the proper time.

hep-th↗

arXiv1999

Possible Physical Manifestation of the Weyl Non-Abelian Gauge Field

On the basis of the Weyl equations of congruent transference, we consider a possible influence of the Weyl non-Abelian gauge field defining the transference on the precession of a gyroscope. Plane-wave solutions to the equations of the non-Abelian gauge field are derived.

hep-th↗

arXiv1998

On Spinor Representations in the Weyl Gauge Theory

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it is a 16-component quantity for which a gauge-invariant Lagrangian is determined. The connexion between the Weyl non-Abelian gauge potential and the Cartan torsion field and the problem of a possible manifestation of the considered interactions are considered.

gr-qc↗

arXiv1997

Integrals of periodic motion for classical equations of relativistic string with masses at ends

Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space $E^1_2$, there are two invariants of that sort, the curvature $K$ and torsion $κ$. For these equations of motion with periodic $κ_i(τ+n l)=κ(τ)$, constants of motion are obtained.

hep-th↗