1,204 research outputs found
The tensor Dirac equation in Riemannian space
We suggest a tensor equation on Riemannian manifolds which can be considered
as a generalization of the Dirac equation for the electron. The tetrad
formalism is not used. Also we suggest a new form of the tensor Dirac equation
with a Spin(1,3) gauge symmetry in Minkowski space.Comment: Latex 19 page
A coordinateless form of the Dirac equation
We present a so called Dirac-type tensor equation (DTTE). This equation is
written in coordinateless form with the aid of differential operators and
. A wave function of DTTE belongs to a minimal left ideal of the
algebra of exterior forms with respect to the Clifford product. We show that a
coordinate form of DTTE is identical to the Dirac equation in a fixed
coordinate system
A model of composite structure of quarks and leptons
In the model every quark or lepton is identified with a quartet of four "more
elementary" particles. One particle in a quartet is a massive spin-0 boson and
other three particles are massless spin-1/2 fermions.Comment: 7 page
A tensor form of the Dirac equation
We prove the following theorem: the Dirac equation for an electron (invented
by P.A.M.Dirac in 1928) can be written as a tensor equation. An equation is
called a tensor equation if all values in it are tensors and all operations in
it take tensors to tensors.Comment: LaTeX, 23 pages I correct mistyping in the third line of the formula
on page 1
Dirac-type tensor equations with non-Abelian gauge symmetries on pseudo-Riemannian space
We suggest a so-called Dirac type tensor equation with nonabelian gauge
symmetry on pseudo-Riemannian space. This equation reproduce some of the
properties of spinor Dirac equation. A geometrical interpretation of results in
terms of Riemannian geometry is given.Comment: 25 page
Dirac-type tensor equations on a parallelisable manyfolds
The goal of this work is to extend Dirac-type tensor equations to a curved
space. We take four 1-forms (a tetrad) as a unique structure, which determines
a geometry of space-time
Notions of determinant, spectrum, and Hermitian conjugation of Clifford algebra elements
We show how the matrix algebra notions of determinant, spectrum, and
Hermitian conjugation transfer to the Clifford algebra and to differential
forms on parallelisable manifolds
General solutions of one class of field equations
We find general solutions of some field equations (systems of equations) in
pseudo-Euclidian spaces (so-called primitive field equations). These equations
are used in the study of the Dirac equation and Yang-Mills equations. These
equations are invariant under orthogonal O(p,q) coordinate transformations and
invariant under gauge transformations, which depend on some Lie groups. In this
paper we use some new geometric objects - Clifford field vector and an algebra
of h-forms which is a generalization of the algebra of differential forms and
the Atiyah-K\"{a}hler algebra.Comment: 22 page
Reconstructing the velocity dispersion profiles from the line-of-sight kinematic data in disc galaxies
We present a modification of the method for reconstructing the stellar
velocity ellipsoid (SVE) in disc galaxies. Our version does not need any
parametrization of the velocity dispersion profiles and uses only one
assumption that the ratio remains constant along the
profile or along several pieces of the profile. The method was tested on two
galaxies from the sample of other authors and for the first time was applied to
three lenticular galaxies NGC~1167, NGC~3245 and NGC~4150 as well as to one Sab
galaxy NGC~338. We found that for galaxies with a high inclination () it is difficult or rather impossible to extract the information
about SVE while for galaxies at an intermediate inclination the procedure of
extracting is successful. For NGC~1167 we managed to reconstruct SVE, provided
that the value of is piecewise constant. We found
for the inner parts of the disc and
for the outskirts. We also obtained a rigid constrain
on the value of the radial velocity dispersion for highly inclined
galaxies and tested the result using the asymmetric drift equation, provided
that the gas rotation curve is available
Local generalization of Pauli's theorem
Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of
anticommuting elements of a real or complexified Clifford algebra of dimension
, is extended to the case, when both sets of elements depend smoothly on
points of Euclidian space of dimension . We prove that in the case of even
there exists a smooth function such that two sets of Clifford algebra
elements are connected by a similarity transformation. All cases of connection
between two sets are considered in the case of odd . Using the equation for
the spin connection of general form, it is shown that the problem of the local
Pauli's theorem is equivalent to the problem of existence of a solution of some
special system of partial differential equations. The special cases ,
and , with more simpler solution of the problem are
considered in detail.Comment: 17 page
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