arXiv subjects
Publications and source records attributed to Ruslan Sharipov.
The closed homogeneous and isotropic universe is considered. The bundles of Weyl and Dirac spinors for this universe are explicitly described. Some explicit formulas for the basic fields and for the connection components in stereographic and in spherical coordinates are presented.
Two explicit formulas for metric connections in the bundle of Dirac spinors are studied. Their equivalence is proved. The explicit formula relating the spinor curvature tensor with the Riemann curvature tensor is rederived.
Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in three-dimensional Euclidean space.
The Higgs field is a central point of the Standard Model supplying masses to other fields through the symmetry breaking mechanism. However, it is associated with an elementary particle which is not yet discovered experimentally. In this short note I suggest a way for expressing the Higgs field through other fields of the Standard Model. If this is the case, being not an independent field, the Higgs field does not require an elementary particle to be associated with it.
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries and self-education groups.
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
The Standard Model of elementary particles is a theory unifying three of the four basic forces of the Nature: electromagnetic, weak, and strong interactions. In this paper we consider the Standard Model in the presence of a classical (non-quantized) gravitation field and apply a bundle approach for describing it.
The Standard Model of the theory of elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three special vector bundles. Connections associated with these vector bundles are studied in this paper. In the Standard Model they are interpreted as gauge fields.
It is known that the Standard Model describing all of the currently known elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In order to implement this symmetry on the ground of a non-flat space-time manifold one should introduce three special bundles. Some aspects of the mathematical theory of these bundles are studied in this paper.
The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed.
It is known that the bundle of Dirac spinors is produced as a direct sum of two bundles - the bundle of chiral spinors and its Hermitian conjugate bundle. In this paper some aspects of metric connections for chiral and Dirac spinors are resumed and their relation is studied.
Some aspects of Dirac spinors are resumed and studied in order to interpret mathematically the P and T operations in a gravitational field.
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
The dynamics and thermodynamics of dislocated crystals are studied within the framework of the nonlinear theory of elastic and plastic deformations.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.