arXiv subjects

S. I. Kruglov

Publications and source records attributed to S. I. Kruglov.

At least 109 records · Page 6Linked to original sources

arXiv2006

Higher Derivative Scalar Field Theory in the First Order Formalism

The scalar field theory with higher derivatives is considered in the first order formalism. The field equation of the forth order describes scalar particles possessing two mass states. The first order relativistic wave equation in the 10-dimensional matrix form is derived. We find the relativistically invariant bilinear form and corresponding Lagrangian. The canonical energy-momentum tensor and density of the electromagnetic current are obtained. Dynamical and non-dynamical components of the wave function are separated and the quantum-mechanical Hamiltonian is found. Projection operators extracting solutions of field equations for definite energy and different mass states of particles are obtained. The canonical quantization of scalar fields with two mass states is performed, and propagators are found in the formalism considered.

hep-th↗

arXiv2006

Effective Action and Electromagnetic Polarizabilities of Nucleons in QCD String Theory

The effective action for baryons in the external electromagnetic fields is obtained on the basis of the QCD string theory. The area law of the Wilson loop integral, the approximation of the Nambu-Goto straight-line strings, and the asymmetric quark-diquark structure of nucleons are used to simplify the problem. The spin-orbit and spin-spin interactions of quarks are treated as a perturbation. With the help of the virial theorem we estimate the mean radii of nucleons in terms of the string tension and the Airy function zeros. On the basis of the perturbation theory in small external electromagnetic fields we derive the electromagnetic polarizabilities of nucleons. The electric and diamagnetic polarizabilities of a proton are $\barα_p= 10\times 10^{-4} fm^3$, $β_p^{dia}=-8\times 10^{-4} fm^3$ and for a neutron we find $\barα_n=4.2\times 10^{-4} fm^3 $, $β_n^{dia}= -5.4\times 10^{-4} fm^3$. Reasonable values of the magnetic polarizabilities $\barβ_p=(5\pm 3)\times 10^{-4} fm^3$, $\barβ_n=(7.6\pm 3)\times 10^{-4} fm^3$ are estimated using the $Δ$ contribution to the paramagnetic polarizability of the nucleons.

hep-ph↗

arXiv2006

On the Hamiltonian Form of Generalized Dirac Equation for Fermions with Two Mass States

Dynamical and non-dynamical components of the 20-component wave function are separated in the generalized Dirac equation of the first order, describing fermions with spin 1/2 and two mass states. After the exclusion of the non-dynamical components, we obtain the Hamiltonian Form of equations. Minimal and non-minimal electromagnetic interactions of particles are considered here.

hep-ph↗

arXiv2005

On the Generalized Dirac Equation for Fermions with Two Mass States

The generalized Dirac equation of the second order, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections are obtained. The first order generalized Dirac equation in the 20-dimensional matrix form and the relativistically invariant bilinear form are derived. We obtain the canonical energy-momentum tensor and density of the electromagnetic current expressed through the 20-component wave function. Minimal and non-minimal electromagnetic interactions of fermions are considered, and the quantum-mechanical Hamiltonian is found. It is shown that there are only causal propagations of waves in the approach considered.

quant-ph↗

arXiv2005

"Square Root" of the Proca Equation: Spin-3/2 Field Equation

New equations describing particles with spin 3/2 are derived. The non-local equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing non-minimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.

hep-th↗

arXiv2005

Resolving parameter degeneracies in long-baseline experiments by atmospheric neutrino data

In this work we show that the physics reach of a long-baseline (LBL) neutrino oscillation experiment based on a superbeam and a megaton water Cherenkov detector can be significantly increased if the LBL data are combined with data from atmospheric neutrinos (ATM) provided by the same detector. ATM data are sensitive to the octant of $θ_{23}$ and to the type of the neutrino mass hierarchy, mainly through three-flavor effects in e-like events. This allows to resolve the so-called $θ_{23}$- and sign($Δm^2_{31}$)-parameter degeneracies in LBL data. As a consequence it becomes possible to distinguish the normal from the inverted neutrino mass ordering at $2σ$ CL from a combined LBL+ATM analysis if $\sin^2 2θ_{13} \gtrsim 0.02$. The potential to identify the true values of $\sin^2 2θ_{13}$ and the CP-phase $δ_{cp}$ is significantly increased through the lifting of the degeneracies. These claims are supported by a detailed simulation of the T2K (phase II) LBL experiment combined with a full three-flavor analysis of ATM data in the HyperKamiokande detector.

hep-ph↗

arXiv2004

Relativistic Wave Equation for Fields with Two Mass and Spin States

I suggest wave equations for the scalar, pseudoscalar, vector, and pseudovector fields with different masses for spin zero and one states. Tensor, matrix, and quaternion formulations of fields with two mass and spin states are considered. This is the generalization of the Dirac-Kähler equation on the case of different masses of fields with spin one and zero. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. Spin projection operators and solutions of equations (for spin one) in the form of matrix-dyads are obtained. The canonical quantization of fields under consideration is studied. The anomalous interaction of the scalar, pseudoscalar, vector, and pseudovector fields with the external electromagnetic field is considered. Three constants which characterize the anomalous magnetic moment and quadrupole electric moment of a particle are introduced.

hep-th↗

arXiv2004

Pair Production of Arbitrary Spin Particles by Electromagnetic Fields

The exact solutions of the wave equation for arbitrary spin particles in the field of the soliton-like electric impulse were obtained. The differential probability of pair production of particles by electromagnetic fields has been evaluated on the basis of the exact solutions. As a particular case, the particle pair producing in the constant and uniform electric field were studied.

hep-ph↗

arXiv2003

Spontaneous CP Violation in the U(3) NJL Model

With the help of the functional integration method, the formation of scalar, pseudoscalar condensates, and dynamical symmetry breaking in the U(3) four-fermion model has been investigated. We show the possibility of spontaneous CP symmetry violation in the model under consideration. The bosonization procedures of the model are performed; the propagators of quarks, scalar and pseudoscalar fields are calculated in one loop approximation. The masses of the scalar and pseudoscalar mesons are evaluated.

hep-ph↗

arXiv2003

Dynamical Symmetry Breaking and Effective Lagrangians in U(n) Four-Fermion Models (n=2,3)

The formation of scalar condensates and dynamical symmetry breaking in the U(n) four-fermion models (for n=2,3) with two coupling constants has been studied by the functional integration method. The bosonization procedures of the models under consideration are performed in one loop approximation. The propagators of fermions, collective Bose-fields (bound states of fermions), as well as the mass formulas for the fermions and bosons, are found. It is shown that a self-consistent consideration of four-fermion models, in the framework of dimension regularization, provides the mass relations for fermions for the case $n\geq 3$. The effective Lagrangian of interacting scalar bosons is also derived for the case n=2.

hep-ph↗

arXiv2003

Effective Lagrangian and Dynamical Symmetry Breaking in the SU(2)XU(1) NJL Model

Dynamical symmetry breaking and the formation of scalar condensates in the SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been studied in the framework of the mean field approximation. The bosonization procedures of the model are performed using the functional integration method. The possibility of the spontaneous CP symmetry breaking in the model under consideration has been shown. The mass spectrum of the bound states of fermions, as well as the effective Lagrangian of interacting scalar and pseudoscalar mesons are obtained.

nucl-th↗

arXiv2003

Dirac-KÄhler Equation

Tensor, matrix and quaternion formulations of Dirac-Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau-Duffin-Kemmer matrix product is considered. We show that the symmetry group of the Dirac-Kähler tensor fields for charged particles is SO(4,2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac-Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac-Kähler fields where the gauge group is the noncompact group under consideration.

hep-th↗

arXiv2002

Trace Anomaly and Quantization of Maxwell's Theory on Non-Commutative Spaces

The canonical and symmetrical energy-momentum tensors and their non-zero traces in Maxwell's theory on non-commutative spaces have been found. Dirac's quantization of the theory under consideration has been performed. I have found the extended Hamiltonian and equations of motion in the general gauge covariant form.

hep-th↗

arXiv2002

Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces

Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of electromagnetic fields on non-commutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the most general gauge covariant form. As a special case, the gauge fixing approach on the basis of Dirac's brackets has been investigated. The problem of the construction of the wave function and physical observables have been discussed.

quant-ph↗

arXiv2002

Exact solutions of the equation for composite scalar particles in quantized electromagnetic waves

The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After diagonalization, we come to equations for free oscillators. As a result, exact solutions of the equation for a particle are found in a plane quantized electromagnetic wave of the arbitrary polarization. As a particular case, the solution for monochromatic electromagnetic waves is considered. The relativistic coherent states of a particle are constructed in the case of the Poisson distribution of photon numbers. In the limit when the average photon number $ $ and the volume $V$ of the quantization trend to infinity (but the photon density $ /V$ remains constant), the wavefunction converts to the solution corresponding to the external classical electromagnetic wave.

hep-ph↗

arXiv2001

Maxwell's Theory on Non-Commutative Spaces and Quaternions

The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane electromagnetic wave is the solution of the system of non-linear wave equations of the second order for the electric and magnetic induction fields. We have found the canonical and symmetrical energy-momentum tensors and their non-zero traces. So, the trace anomaly of the energy-momentum tensor was obtained in electrodynamics on non-commutative spaces. It was noted that the dual transformations of electromagnetic fields on non-commutative spaces are broken.

hep-th↗

arXiv2001

Bosonic Fields with Two Mass and Spin States

We consider the bosonic fields which describe a particle which may exist in states with spins one and zero with different masses. All the linearly independent solutions of the equation for a free particle are obtained in the form of the projection matrix-dyads (density-matrices). The interaction with anomalous magnetic dipole and quadruple electric moments of a particle is studied. The Hamiltonian form of the first order equation has been investigated.

hep-th↗

arXiv2001

Wave Equation Solutions and Pair Production for Arbitrary Spin Particles

We investigate the theory of particles with arbitrary spin and magnetic moment in the Lorentz representation (0,s)X(s,0) in an external constant and uniform electromagnetic field. We obtain the density matrix of free particles in pure spin states. The differential probability of pair producing particles with arbitrary spin by an external constant and uniform electromagnetic field is found using the exact solutions. We calculate the imaginary and real parts of the Lagrangian in an electromagnetic field that takes into account the vacuum polarization.

hep-ph↗