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S. I. Kruglov

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

At least 91 records · Page 5Linked to original sources
arXiv2013

Modified wave equation for spinless particles and its solutions in an external magnetic field

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated.

hep-th↗
arXiv2013

Modified Dirac equation with Lorentz invariance violation and its solutions for particles in an external magnetic field

The second-order modified Dirac equation leading to the modified dispersion relation due to the Lorentz invariance violation corrections is suggested. The equation is formulated in the 16-component first- order form. I have obtained the projection matrix extracting solutions of the equation with definite spin projections which can be considered as the density matrix for pure spin states. Exact solutions of the equation are found for particles in the external constant and uniform magnetic field. The synchrotron radiation radius within the novel modified Dirac equation is estimated.

gr-qc↗
arXiv2012

On superluminal fermions within the second derivative equation

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy-momentum tensor are found. The minimal and non-minimal electromagnetic interactions of fermions are considered and Schrödinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.

hep-ph↗
arXiv2011

Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism

Field theory of massive and massless vector particles is considered in the first-order formalism. The Hamiltonian form of equations is obtained after the exclusion of non-dynamical components. We obtain the canonical and symmetrical Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken in the massive case but in the massless case the modified dilatation current is conserved. The canonical quantization is performed and the propagator of the massive fields is found in the Duffin - Kemmer - Petiau formalism.

hep-th↗
arXiv2011

A note on generalized electrodynamics

The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante energy-momentum tensors are found. The dilatation current is obtained and we demonstrate that the theory possesses the dilatation symmetry. The matrix Schrödinger form of equations is derived. The non-minimal interaction in curved space-time is introduced and equations are considered in Friedmann - Robertson - Walker background. We obtain some solutions of equations for the vector field.

hep-th↗
arXiv2010

Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found.

math-ph↗
arXiv2010

On generalized Born--Infeld electrodynamics

The generalized Born--Infeld electrodynamics with two parameters is investigated. In this model the propagation of a linearly polarized laser beam in the external transverse magnetic field is considered. It was shown that there is the effect of vacuum birefringence, and we evaluate induced ellipticity. The upper bounds on the combination of parameters introduced from the experimental data of BRST and PVLAS Collaborations were obtained. When two parameters are equal to each other, we arrive at Born--Infeld electrodynamics and the effect of vacuum birefringence vanishes. We find the canonical and symmetrical Belinfante energy-momentum tensors. The trace of the energy-momentum tensor is not zero and the dilatation symmetry is broken. The four-divergence of the dilatation current is equal to the trace of the Belinfante energy-momentum tensor and is proportional to the parameter (with the dimension of the field strength) of the model. The dual symmetry is also broken in the model considered.

hep-th↗
arXiv2010

Note on Dirac--Kähler massless fields

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac--Kähler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.

hep-th↗
arXiv2010

Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism

The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin projections are obtained, and we find the density matrix for the massive state. The $13\times 13$-matrix Schrodinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.

hep-th↗
arXiv2010

Generalized Weinberg-Tucker-Hammer equations in the Petiau-Duffin-Kemmer form

Massive and massless vector particles, in the framework of generalized Weinberg-Tucker-Hammer equations, are considered in the Petiau-Duffin-Kemmer formalism. We obtain solutions of equations in the form of matrix-dyads. The Lagrangian is defined in the matrix form and the conserved electric current and the energy-momentum tensor are obtained. The canonical quantization is performed and the propagator of massive fields is found in the formalism considered.

math-ph↗
arXiv2010

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.

hep-th↗
arXiv2009

On First-Order Generalized Maxwell Equations

The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the canonical and symmetrical Belinfante energy-momentum tensors. It is shown that the traces of the energy-momentum tensors are not equal to zero and the dilatation symmetry is broken in the theory considered. The matrix Hamiltonian form of equations is obtained after the exclusion of the nondynamical components. The canonical quantization is performed and the propagator of the fields is found in the first-order formalism.

hep-th↗
arXiv2009

On Possible Light-Torsion Mixing in Background Magnetic Field

The interaction of the light with propagating axial torsion fields in the presence of an external magnetic field has been investigated. Axial torsion fields appearing in higher derivative quantum gravity possess two states, with spin one and zero, with different masses. The torsion field with spin-0 state is a ghost that can be removed if its mass is infinite. We investigate the possibility when the light mixes with the torsion fields resulting in the effect of vacuum birefringence and dichroism. The expressions for ellipticity and the rotation of light polarization axis depending on the coupling constant and the external magnetic field have been obtained.

hep-ph↗
arXiv2008

Vacuum Birefringence Caused by Arbitrary Spin Particles

We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam are evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.

hep-ph↗
arXiv2008

On Torsion Fields in Higher Derivative Quantum Gravity

We consider axial torsion fields which appear in higher derivative quantum gravity. It is shown, in general, that the torsion field possesses states with two spins, one and zero, with different masses. The first-order formulation of torsion fields is performed. Projection operators extracting pure spin and mass states are given. We obtain the Lagrangian in the framework of the first order formalism and energy-momentum tensor. The effective interaction of torsion fields with electromagnetic fields is discussed. The Hamiltonian form of the first order torsion field equation is given.

gr-qc↗
arXiv2007

Effective Lagrangian at Cubic Order in Electromagnetic Fields and Vacuum Birefringence

The effective Lagrangian of electromagnetic fields at the cubic order in field strength has been considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical energy-momentum tensors and show that they possess non-zero traces. The propagation of a linearly polarized laser beam in the external transverse magnetic field is investigated. We evaluate the induced ellipticity which allows us to obtain a constraint on parameters introduced from the PVLAS experimental data.

hep-ph↗
arXiv2007

Higher Derivative Fermionic Field Equation in the First Order Formalism

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found which extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and non-minimal (anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first order equation has been obtained.

hep-ph↗