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Valeri V. Dvoeglazov

Publications and source records attributed to Valeri V. Dvoeglazov.

At least 19 recordsLinked to original sources
arXiv2018

A Note on Non-commutativity

Ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of this subject on quantum mechanics and the classical/quantum field theory. Surprisingly, some commutators of operators of space-time 4-coordinates and those of 4-momenta are not equal to zero. Notes added in the Abstract: Two iterated limits are not equal each other, in general. Thus, we present an example when the massless limit of the function of E, p, m does not exist in some calculations within quantum field theory.

math-ph↗
arXiv2010

The Construction of Quantum Field Operators: Something of Interest

We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is paid to the chiral theories, and to the method of the Lorentz boosts.

math-ph↗
arXiv2009

Relativistic Equations for Spin Particles: What Can We Learn From Noncommutativity?

We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can the introduction of non-commutativity give us. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.

hep-th↗
arXiv2009

P, C and T for Truly Neutral Particles

We present a realization of a quantum field theory, envisaged many years ago by Gelfand, Tsetlin, Sokolik and Bilenky. Considering the special case of the (1/2,0)+(0,1/2) field and developing the Majorana construct for neutrino we show that a fermion and its antifermion can have the same properties with respect to the intrinsic parity (P-) operation. The transformation laws for C- and T- operations have also been given. The construct can be applied to explanation of the present situation in neutrino physics. The case of the (1,0)+ (0,1) field is also considered.

hep-th↗
arXiv2007

Antisymmetric Tensor Fields, 4-Vector Fields, Indefinite Metrics and Normalization

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2J+1) theory are found. Next, we introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed. The problem of indefinite metrics, particularly, in quantization of 4-vector fields is clarified.

math-ph↗
arXiv2007

Fermion-fermion and boson-boson amplitudes: surprising similarities

Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j+1)-component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p_0^2 - p^2=M^2, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T-matrices for the fermion case and the boson case. However, certain differences are found. Possible physical applications are discussed.

math-ph↗
arXiv2007

The Barut Second-Order Equation: Lagrangian, Dynamical Invariants and Interactions

The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the 70s. It permits to explain the mass splitting of leptons (e,mu,tau). Recently, the interest has grown to this model (see, for instance, the papers by S. Kruglov and J. P. Vigier et al). We continue the research deriving the equation from the first principles, finding dynamical invariants for this model, investigating the influence of potential interactions.

hep-th↗
arXiv2007

Modified Bargmann-Wigner Formalism (Bosons of Spin 1 and 2)

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2J+1) theory are found. Next, we introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed.

hep-th↗
arXiv2005

The Barut Second-Order Equation, Dynamical Invariants and Interactions

The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s. It permits to explain the mass splitting of leptons e,mu,tau. Recently, the interest has grown to this model (see, for instance, the papers by S. Kruglov and J. P. Vigier et al.). We continue the research deriving the equation from the first principles, finding the dynamical invariants for this model, investigating the influence of the potential interactions.

math-ph↗
arXiv2004

Helicity Basis for Spin 1/2 and 1, and Discrete Symmetry Operations

We study the theory of the (1/2,0)+(0,1/2) and (1,0)+(0,1) representations of the Lorentz group in the helicity basis. The helicity eigenstates are not the parity eigenstates. This is in accordance with the idea of Berestetskii, Lifshitz and Pitaevskii. The properties of the helicity eigenstates with respect to the charge conjugation and the CP- conjugation are also considered.

math-ph↗
arXiv2004

A Note on the Lorentz Transformations for Photon

We discuss transormation laws of electric and magnetic fields under Lorentz transformations, deduced from the Classical Field Theory. It is found that we can connect the resulting expression for a bivector formed with those fields, with the expression deduced from the Wigner transformation rules for spin-1 functions of massive particles. This mass parameter should be interpreted because the constancy of speed of light forbids the existence of the photon mass.

physics.class-ph↗
arXiv2004

Helicity Basis for Spin 1/2 and 1

We study the theory of the (1/2,0)+(0,1/2) and (1,0)+(0,1) representations in the helicity basis. The helicity eigenstates are not the parity eigenstates. This is in accordance with the idea of Berestetskii, Lifshitz and Pitaevskii. The behaviour of the helicity eigenstates with respect to the charge conjugation, CP- conjugation is also different comparing with the parity eigenstates.

physics.hist-ph↗
arXiv2003

Helicity Basis and Parity

We study the theory of the (1/2,0)+(0,1/2) representation in helicity basis. Helicity eigenstates are not the parity eigenstates. This is in accordance with the consideration of Berestetskii, Lifshitz and Pitaevskii. Relations to the Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new form of the parity operator is proposed. It commutes with the Hamiltonian.

math-ph↗
arXiv2003

Is the Space-Time Non-Commutativity Simply Non-Commutativity of Derivatives?

Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of this observation on the quantum mechanics and classical/quantum field theory. Surprisingly, some commutators of the coordinate-dependent operators are not equal to zero. Therefore, we try to provide mathematical foundations to the modern non-commutative theories. We also indicate possible applications in the Dirac-like theories.

math-ph↗
arXiv2003

Base de Helicidad y Paridad

We study the theory of the Lorentz group (1/2,0)+(0,1/2) representation in the helicity basis of the corresponding 4-spinors. As Berestetski, Lifshitz and Pitaevskii mentioned, the helicity eigenstates are not the parity eigenstates. Relations with the Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new form of the parity operator (which commutes with the Hamiltonian) is proposed in the Fock space.

hep-th↗