arXiv subjects

L. A. Glinka

Publications and source records attributed to L. A. Glinka.

16 recordsLinked to original sources

arXiv2009

New Approach to Quantization of Cosmological Models

We propose the new quantization of homogenous cosmological models. Four fundamental methods are applied to the cosmological model and efficiently jointed. The Dirac method for constrained systems is used, then the Fock space is built and the second quantization is carried out. Finally, the diagonalization ansatz, which is a combination of the Bogoliubov transformation method and the Heisenberg equation of motion, is formulated. The temperature of quantum cosmological model is introduced.

gr-qc↗

arXiv2009

Global One-Dimensionality conjecture within Quantum General Relativity

The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the quantum geometrodynamics. By dimensional reduction the resulting theory is presented in the form of the Dirac equation, and application of the Fock quantization with the diagonalization procedure yields construction of the appropriate quantum field theory. The 1D wave function is derived, the corresponding 3-dimensional manifolds are discussed, and physical scales are associated with quantum correlations.

gr-qc↗

arXiv2009

CP violation, massive neutrinos, and its chiral condensate: new results from Snyder noncommutative geometry

The Snyder model of a noncommutative geometry due to a minimal scale $\ell$, e.g. the Planck or the Compton scale, yields $\ell^2$-shift within the Einstein Hamiltonian constraint, and $γ^5$-term in the free Dirac equation violating CP symmetry manifestly. In this paper the Dirac equation is reconsidered. In fact, there is no any reasonable cause for modification of the Minkowski hyperbolic geometry of a momentum space. It is the consistency -- in physics phase space, spacetime (coordinates), and momentum space (dynamics) are independent mathematical structures. It is shown that the modified Dirac equation yields the kinetic mass generation mechanism for the left- and right-handed Weyl chiral fields, and realizes the idea of neutrinos receiving mass due to CP violation. It is shown that the model is equivalent to the gauge field theory of composed two 2-flavor massive fields. The global chiral symmetry spontaneously broken into the isospin group leads to the chiral condensate of massive neutrinos. This result is beyond the Standard Model, but in general can be included into the theory of elementary particles and fundamental interactions.

hep-ph↗

arXiv2009

Energy renormalization and integrability within the massive neutrinos model

In this paper the massive neutrinos model arising due to the Snyder noncommutative geometry, proposed recently by the author is partially developed. By straightforward calculation it is shown that the masses of the chiral left- and right-handed Weyl fields treated as parameters fixed by experiments, lead to the consistent physical picture of the noncommutative geometry, and consequently yield renormalization of an energy of a relativistic particle and exact integrability within the proposed model. This feature of the model in itself both defines and emphasizes its significance and possible usefulness for both theory as well as phenomenology for high energy physics and astrophysics.

hep-ph↗

arXiv2009

On some consequences of the Snyder-Sidharth deformation of Special Relativity

The hypothesis on a minimal scale existence in the Universe leads to noncommutative geometry of Spacetime and thence to a modification of the Special Relativity constraint. Sidharth has deduced that this is equivalent to the Lorentz symmetry violation. This latter consideration was also used by Glashow, Coleman and other scholars though based on purely phenomenological models that have been suggested by the observation of Ultra High Energy Cosmic Rays and Gamma Bursts. On the other hand a parallel development has been the proposal of a small but nonzero photon mass $m_γ>0$ by some authors including Sidharth, such a mass being within experimentally allowable limits. This too leads to a small violation of the Lorentz symmetry observable in principle in very high energy gamma rays, as in fact is claimed. In this paper we study the Snyder--Sidharth Hamiltonian and briefly comment the Dirac--Sidharth Hamiltonian, that is a possible explanation for observable violation of the Lorentz symmetry.

hep-th↗

arXiv2008

Macrostates thermodynamics and its stable classical limit in Global One-Dimensional Quantum General Relativity

Global One--Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of three-dimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3+1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirms that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.

gr-qc↗

arXiv2008

Quantum gravity as the way from spacetime to space quantum states thermodynamics

Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation the thermodynamic information is actually quantum gravity. We propose new realization of this old idea by studying the canonical 3+1 Dirac-ADM approach to pseudo-Riemannian (Lorentzian) manifold of General Relativity. We derive the Wheeler-DeWitt theory as the Global One-Dimensional classical field theory of the Bose field associated with embedded 3-space, where Wheeler's superspace metric is absent. The classical theory is discussed, some deductions on tachyon state, Dark Energy density and cosmological constant are included. Reduction to 1st order evolution is carried out, and quantum theory by the second quantization in the Fock space of creators and annihilators is constructed by employing the Heisenberg equation and the bosonic Bogoliubov transformation for diagonalization. In result we find the static reper with stable vacuum, where quantum states of 3-space can be considered, and finally space quantum states thermodynamics is formulated.

gr-qc↗

arXiv2008

Multiparticle Quantum Cosmology

Fock space quantization of Hamiltonian constraints of General Relativity and thermodynamics of quantum states for flat Friedmann-Lemaitre-Robertson-Walker metrics is presented.

gr-qc↗

arXiv2008

Higgs Particle Mass in Cosmology

A version of the Standard Model is considered, where the electroweak symmetry breaking is provided by cosmological initial data given for the zeroth Fourier harmonic of the Higgs field $<ϕ>$. The initial data symmetry breaking mechanism removes the Higgs field contribution to the vacuum energy density, possible creation of monopoles, and tachion behavior at high energies, if one imposes an ``inertial'' condition on the Higgs potential $\textsf{V}_{\rm Higgs}(<ϕ>)=0$. The requirement of zero radiative corrections to this {\em inertial} condition coincides with the limiting point of the vacuum stability in the Standard Model. The latter together with the direct experimental limit gives the prediction for the mass of the Higgs boson to be in the range $114 < m_h \lsim 134$ GeV.

hep-ph↗

arXiv2007

On quantum cosmology as field theory of bosonic string mass groundstate

The Quantum Cosmology can be understand as the theory of an one object that is the Universe described in terms of fundamental mass groundstate of the free boson string, that is a tachyon - a hypothetical particle with negative mass square, which has linear velocity more than the velocity of light c. From this fact it is clear that whole information about physics of our Universe is focused on studying of this untypical particle physics. In this paper this point of view is touched up on. As the general-relativistic model of our Universe we study the Einstein-Friedmann Spacetime. Firstly, the way of canonical quantization beginning from first quantization of the Dirac Hamiltonian constraints up to the second quantization by the Von Neumann-Araki-Woods quantization in the Fock space is briefly discussed. We show that using of the Bogoliubov-Heinsenberg static operator basis leads to formulation of the second quantization of the considered free boson string in terms of the monodromy in the Fock space. Finally, we propose some specific model of the Universe - the extremal tachyon mass model, and in frames of its the Hubble evolution parameter, the equation of state for Dark Matter in the Universe, and the temperature of our Universe are concluded.

gr-qc↗

arXiv2007

Many-Particle Quantum Cosmology

The Einstein-Friedmann Universe as whole quantum object can be treated as bosonic string mass groundstate, called a tachyon, having negative mass square and a speed more than the speed of light. I present a brief review of results obtained from this point of view called Many-Particle Quantum Gravity approach - the monodromy problem in the Fock space, thermodynamics of the Universe, and the extremal tachyon mass model.

hep-th↗

arXiv2007

Hamiltonian Unification of General Relativity and Standard Model

The Hamiltonian approach to the General Relativity and the Standard Model is studied in the context of its consistency with the Newton law, the Higgs effect, the Hubble cosmological evolution and the Cosmic Microwave Background radiation physics. The version of the Higgs potential is proposed, where its constant parameter is replaced by the dynamic zeroth Fourier harmonic of the very Higgs field. In this model, the extremum of the Coleman--Weinberg effective potential obtained from the unit vacuum--vacuum transition amplitude immediately predicts mass of Higgs field and removes tremendous vacuum cosmological density. We show that the relativity principles unambiguously treat the Planck epoch, in the General Relativity, as the present-day one. It was shown that there are initial data of the Electro-Weak epoch compatible with supposition that all particles in the Universe are final products of decays of primordial Higgs particles and W-, Z-vector bosons created from vacuum at the instant treated as the "Big-Bang".

gr-qc↗

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↗

arXiv2007

Hamiltonian Approach to Conformal Coupling Scalar Field in the General Relativity

The dynamic status of scalar fields is studied in the Hamiltonian approach to the General Relativity. We show that the conformal coupling of the scalar field violates the standard geometrical structure of the Einstein equations in GR and their solutions including the Schwarzschild one and the Newton static interaction. In order to restore the standard geometrical structure of GR, the scalar field is mixed with the scale metric component by the Bekenstein type transformation. This "scalar-scale" mixing converts the conformal coupling scalar field with conformal weight (n= -1) into the minimal coupling scalar field with zero conformal weight (n=0) called a "scalar graviton". Cosmological consequences of the "scalar-scale" mixing are considered in the finite space-time by extraction of the zero mode (homogeneous) harmonics of a "scalar graviton". The classical dynamics of "scalar graviton" testifies about a tremendous contribution of evolution at the beginning in the form of the rigid state.

gr-qc↗

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↗