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V. P. Neznamov

Publications and source records attributed to V. P. Neznamov.

54 records · Page 3Linked to original sources
arXiv2011

I. The Isotopic Foldy-Wouthuysen Representation and Chiral Symmetry

The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix, these equations possess chiral invariance irrespective of whether fermions have mass or are massless. The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions. In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P - symmetry). This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.

physics.gen-ph↗
arXiv2011

II. The Standard Model in the Isotopic Foldy-Wouthuysen Representation without Higgs Bosons in the Fermion Sector. Spontaneous Breaking of Parity and "Dark Matter" Problems

The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(2)xU(1) - invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently, it is not necessary to introduce interactions between Higgs bosons and fermions. The study discusses a possible relation between spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles of "dark matter".

physics.gen-ph↗
arXiv2011

Atoms and Forces of Interaction Between Elementary Particles in the Expanding Universe

The earlier developed algorithm for constructing a self-conjugate Hamiltonian in the η-representation for Dirac particles interacting with a general gravitational field is extended to the case of electromagnetic fields. This Hamiltonian is applied to the case when the gravitational field describes the spatially flat Friedmann model, and the electromagnetic field is the Coulomb potential extended to the case of this model. The analysis of atomic systems and electromagnetic forces of interaction under the conditions of spatially flat expansion of the universe has demonstrated that the system of atomic levels does not change with cosmological time. Spectral lines of atoms in the spatially flat Friedmann model are identical at different points of cosmological time. In this case the redshift is stipulated entirely by the growth of wavelength of photons at movement in the expending universe. At the same time force of interaction between elementary particles can change with expansion of the universe.

gr-qc↗
arXiv2011

Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields

Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the η-representation gives the transformation of the Schroedinger equation for nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the η-representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.

gr-qc↗
arXiv2010

Electron Self-energy in Pseudo-Hermitian Quantum Electrodynamics with a Maximal Mass M

The electron self-energy (self-mass) is calculated on the basis of the model of quantum field theory with maximal mass M, developed by V.G.Kadyshevsky et al. within the pseudo-Hermitian quantum electrodynamics in the second order of the perturbation theory. In theory, there is the natural cut-off of large transmitted momentum in intermediate states because of presence of the universal mass M. As a result, the electron self-mass is finite and depends on the transmitted maximum momentum. Two interpretations of the obtained results are possible at defined M and A. The first interpretation allows confirming quantitatively the old concept of elementary particle mass sources defined by interaction of particles with self-gauge fields. The second interpretation results in the possibility not to renormalize the mass (at least in the second order of perturbation theory) owing to the zero mass operator.

physics.gen-ph↗
arXiv2010

Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields

The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are non-unique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians, but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.

gr-qc↗
arXiv2010

Calculation of Matrix Elements in the Foldy-Wouthuysen Representation

The paper compares the methods used to calculate matrix elements of the operator of radail electron coordinates in an arbitrary order in the Foldy-Wouthuysen representation and with the use of the Dirac equation for 1s-states of the hydrogen-like and helium-like ions of transuranic elements. The obtained analytical and numerical results for 1s-states of the hydrogen-like and helium-like ions proves that the wave function reduction requirement is met with transformation to the Foldy-Wouthuysen representation and confirms that matrix elements can be calculated using only one component (either upper, or lower) of the Dirac bispinor wave function.

physics.gen-ph↗
arXiv2010

The Dirac Equation in the Model With a Maximal Mass

In paper within the model with a maximal mass M and with use of anti de Sitter space is considered the Dirac equation properties for a fermion of mass m on the mass surface. The paper shows that free Hamiltonian and Hamiltonian with interaction are pseudo-Hermitian. If we accept the appropriate rules of use of pseudo-Hermitian Hamiltonians, we can construct the consistent quantum theory with final results obtained using the ordinary Dirac equation.

physics.gen-ph↗
arXiv2009

Foldy-Wouthyusen wave functions and conditions of transformation between Dirac and Foldy-Wouthuysen representations

The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved. The connection between wave functions in the two representations is derived. The results obtained allows calculating expectation values of operators corresponding to main classical quantities.

math-ph↗
arXiv2008

The Standard Model and Fermion Masses

The paper formulates the Standard Model with massive fermions without introduction of the Yukawa interaction of Higgs bosons with fermions. For invariance to be preserved in the newly stated theory, the covariant derivative should be generalized, as follows. With such approach, Higgs bosons are responsible only for the gauge invariance of the boson sector of the theory and interact only with gauge bosons, gluons and photons.

hep-th↗
arXiv2008

The Necessary and Sufficient Conditions for Transformation from Dirac Representation to Foldy-Wouthuysen Representation

The paper describes conditions for transformation from the Dirac representation to the Foldy-Wouthuysen representation. The necessary condition is the block-diagonal transformation of Hamiltonian relative to the upper and lower components of the wave function. The sufficient condition is the wave function transformation law described by relation (6). It has been demonstrated that the unitary transformations offered by the authors of the papers [14], [15], [16], [17] do not satisfy the sufficiency condition (6) and, hence, they are not the Foldy-Wouthuysen transformations. In applications, the matrix elements of any operator in the FW representation can be calculated, according to (6), using the normalized two-component wave functions in the Dirac representation known for the given problem.

math-ph↗
arXiv2004

A Standard Model in Foldy-Wouthuysen Representation

The paper formulates a standard model in the Foldy-Wouthuysen representation using previously developed approaches as applied to quantum electrodynamics. The formulation of the theory in the FW representation does not require obligatory interaction of Higgs bosons with fermions for SU(2) invariance. In this approach the Higgs boson spectrum is narrowed significantly: the Higgs bosons are responsible only for the gauge invariance of the theory and interact only with gauge bosons.

hep-th↗
arXiv2004

On the theory of interacting fields in Foldy-Wouthuysen representation

The paper considers quantum electrodynamics (QED) and weak interaction of elementary particles in the lower orders of the perturbation theory using nonlocal Hamiltonian in the Foldy-Wouthuysen (FW) representation. Feynman rules in the FW representation are specified, specific QED processes are calculated. Cross sections of Coulomb scattering of electrons, Muller scattering, Compton effect, electron self-energy, vacuum polarization, anomalous magnetic moment of electron, Lamb shift of atomic energy levels are calculated. The possibility of the scattering matrix expansion in powers of the coupling constant, in which matrix elements contain no terms with fermion propagators, is demonstrated for external fermion lines corresponding to real particles (antiparticles). It is shown that a method to include the interaction of real particles with antiparticles in the FW representation is to introduce negative mass particles and antiparticles to the theory. The theory is degenerate with respect to the particle (antiparticle) mass sign, however the masses of the particle and antiparticle interacting with each other should be of opposite sign. QED in the FW representation is invariant under C, P, T inversions. The weak interaction breaks the C and P invariance, but preserves the combined CP parity. In the theory there is a possibility to relate the break of CP invariance to total or partial removal of the degeneracy in particle (antiparticle) mass sign.

hep-th↗
arXiv2004

Anomalous magnetic moment and Lamb shift in the second order of the perturbation theory with finite electron mass renormalization in quantum electrodynamics

The paper determines the anomalous magnetic moment and Lamb energy level shift in the second order of the perturbation theory using the algorithm of self-energy expression regularization in quantum electrodynamics that meets the relativistic and gauge invariance requirements; the comparison is made to the associated conventional quantum electrodynamics results. A limiting 4-impulse with an infinitely large temporal component and limited value of spatial components that depend quite weakly on the Dirac particle impulse variation is introduced within the algorithm. The answer in regard to the agreement between the experimental data and results of the calculations by the algorithm of this paper will be given by the calculations of the next order of the perturbation theory which are being planned for the nearest future.

hep-th↗