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Nikolay Marchuk

Publications and source records attributed to Nikolay Marchuk.

10 recordsLinked to original sources
arXiv2026

Gauge invariant generalizations of the Proca equation and the Yang-Mills-Proca equation

The Proca equations (1936) are used in quantum field theory to describe vector bosons (spin 1) with a nonzero mass. The Proca equations are not gauge invariant. In contrast to Stueckelberg's approach (1938), this article presents a gauge invariant generalization of the Proca equation by introducing an additional vector field into the Proca equation. The results are extended to the Yang-Mills-Proca equations, leading to equations with non-Abelian gauge symmetry.

math-ph↗
arXiv2026

Sketch of a Gauge Model of Gravity with SU(2) Symmetry in Minkowski space

We propose a gauge model with the SU(2) symmetry, which describes a gravitational interaction of fundamental fermions (leptons and quarks) in the Minkowski space. In the Standard Model one uses a Dirac-Yang-Mills system of equations with U(2) gauge symmetry for electroweak interactions and with SU(3) gauge symmetry for QCD interactions. A key idea of the model is to use the Dirac-type equation (invented in 2002) instead of the standard Dirac equation. This Dirac-type equation has an additional SU(2) gauge symmetry. The Yang-Mills field, which corresponds to this SU(2) symmetry, we identify with the gravitational field of interacted fundamental fermions. Some elements of Clifford analysis are used in the model.

math-ph↗
arXiv2025

Sketch of a gauge model of gravity with SU(2) symmetry on a Lorentzian manifold with tetrad

A gauge model with SU(2) symmetry is proposed to describe the gravitational interaction of fundamental fermions (leptons and quarks) on a Lorentzian manifold with a tetrad. From the system of Dirac-Yang-Mills equations underlying the Standard Model, we arrive at a model system of Dirac-Lanczos-Yang-Mills equations, written using second-order matrices. This system of equations has an additional gauge symmetry with respect to the unitary group SU(2). The Yang-Mills field associated with this gauge group is interpreted as the gravitational field interacting with fundamental fermions.

physics.gen-ph↗
arXiv2019

Model Dirac and Dirac-Hestenes equations as covariantly equipped systems of equations

We define a new class of partial differential equations of first order (complex covariantly equipped systems of equations), which are invariant with respect to (pseudo)orthogonal changes of cartesian coordinates of (pseudo)euclidian space. It is shown that for pseudoeuclidian spaces of signature (1,n-1) covariantly equipped systems of equation can be written in the form of Friedrichs symmetric hyperbolic systems of equations of first order. We prove that Dirac and Dirac-Hestenes model equations belong to the class of covariantly equipped systems of equations.

math-ph↗
arXiv2016

Classification of extended Clifford algebras

Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford algebras is closed with respect to the tensor product.

math.RA↗
arXiv2011

Generalized exterior algebras

Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as 0-metric exterior algebra. Clifford algebra can be considered as 1-metric exterior algebra. $N$-metric exterior algebras for $N\geq2$ can be considered as generalizations of the Grassmann algebra and Clifford algebra. Specialists consider models of gravity that based on a mathematical formalism with two metric tensors. We hope that the considered in this paper 2-metric exterior algebra can be useful for development of this model in gravitation theory. Especially in description of fermions in presence of a gravity field.

math-ph↗