Gravitational interaction in a model of nonlinear spinor theory with derivatives of the fundamental fields

To eliminate the difficulties that arise when particles of high spin (J 2) are treated in nonlinear spinor field theory, it is proposed to include terms with derivatives of the fundamental fields in the self-interaction Lagrangian of the subparticles. It is shown that with this generalization the four-fermion model of nonlinear spinor theory describes the gravitational interaction of subparticles in the approximation of single-graviton exchange. A relation between the gravitational constant and the parameters of the model is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 79–85, August, 1977.I thank D. D. Ivanenko for a helpful discussion of this work.     

Gravitation and nonlinear spinor theory

In the framework of a single model of nonlinear spinor theory of matter, an attempt is made to describe the gravitational interaction. It is shown that the scattering amplitude of two primary fermions contains a contribution corresponding to one-graviton exchange. A relation between the gravitational constant and the mass of a subparticle is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 75–81, September, 1974.I thank Professor D. D. Ivanenko and A. I. Naumov for their interest and helpful discussions.     

Cosmological solutions foe a spinor field in the general theory of relativity

We consider models of the universe containing linear and nonlinear spinor matter. It is assumed that the linear spinor matter is described by the generally covariant Dirac equation, and the nonlinear by the generally covariant Ivanenko-Heisenberg equation.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 68–71, December, 1973.     

Spinor theory of general relativity without elementary gravitons

We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ_μ^α. Our theory has no elementary spin-2 quanta, but does reproduce Einstein's general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.     

The nonlinear group representation method in the nonlinear spinor theory

Nonlinear spinor equations are derived in the paper by the nonlinear symmetry-group representation method. The basic field transforms according to the linear spinor representation of the orthochronous Lorentz group Lt. The internal symmetry group G^r is realized as a group of nonlinear transformations of the field . The invariant nonlinear spinor equations constituting the group G^r are found in terms of the covariant derivative. The group SU(2) is considered as an example.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–55, December, 1972.The author thanks D. D. Ivanenko and D. F. Kurdgelaidze for stimulating discussions and support.     

Spinor fields in the nonsymmetric,non-Abelian Kaluza-Klein theory

Spinor fields are considered in the framework of the nonsymmetric Kaluza-Klein theory and the nonsymmetric Jordan-Thiry theory (in non-Abelian case). Dipole moments for fermions of value 10^–31 and pseudomass-like terms are found.     

On the analogy between neutrino and nonlinear spinor fields

This paper considers some aspects of the neutrino dynamics i.e. connection between neutrino and nonlinear spinor fields (due to torsion).     

Interacting fields in general relativity theory

The direct interaction of a massless neutral scalar field with an electromagnetic field is investigated with regard for the proper gravitational field. The interaction Lagrangian is chosen in the form L_int=FF, =e–1, where the parameter characterizes the interaction force. Exact static spherically and cylindrically symmetric solutions are obtained. A solution with a finite total field energy is extracted. A comparison is made with the corresponding system in flat space-time. It is concluded that the gravitational field performs a regulatory function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–30, September, 1977.The authors are indebted to Yu. S. Vladimirov for valuable comments.     

Kinetic equation in the general theory of relativity

An attempt is made to discover the physical content of the general-relativistic theory of gases. Under an invariant interpretation of the collision term, this theory does not satisfy the correspondence principle for classical theory. The collision term in the classical Boltzmann form is meaningful only in an isolated reference frame realized by a locally inertial frame with the origin at the collision point. With this formulation of the kinetic equations, the class of equilibrium states in GR expands considerably and also covers nonstationary distributions. A specific example of such a distribution that is locally Maxwellian is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 72–76, February, 1979.In conclusion, the author considers it his pleasant duty to thank Prof. N. A.Chernikov for useful discussion of certain problems touched on this paper, and A. V. Zakharov, who made this result of his article koown to the author.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

On stability of stationary soliton solutions to the nonlinear field equation in a general spinor model

The problem of determining the stability domain (in Lyapunov sense) of three dimensional soliton solutions is considered. Some necessary conditions for stability are obtained and it is shown that the boundary of the stability domain is defined by the inequality ωⁱω^k(?Qⁱ/?ω_k < 0.     

Exact plane-symmetric solutions of the nonlinear equations of a spinor field in the theory of gravitation

We obtain exact plane-symmetric solutions of the spinor field equations with a nonlinear term that is an arbitrary functions of the invariant and with the self-gravitational field taken into account. Conditions are formulated for which the initial system of Einstein's equation and the spinor field equations with a power-law nonlinearity have regular solutions with localized (negative) spinor field energy density: so-called soliton-like solutions. Exact solutions of the spinor field equations are also obtained in flat space—time in this case and it is shown that the initial system of equations does not have soliton-like solutions. Hence the self-gravitational field plays a crucial (regularizing) in soliton-like solutions of the nonlinear spinor field equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 63–68, August, 1995.     

Spinor fields and symmetries of the spacetime

We show that in the background of a stationary and axisymmetric black hole, there is a particular spinor field whose “conserved current” interpolates between the null Killing vector on the horizon and the time Killing vector at the spatial infinity. The spinor field only needs to satisfy a very general and simple constraint.     

The geodesic equation in five-dimensional relativity theory of Kaluza-Klein

In five-dimensional relativity theory of Kaluza-Klein the projection of the 5-geodesic equation is discussed in detail. The scalar occurring within this framework is first assumed to be variable. A simple classification of 5-geodesics is found and pictured with the help of a deformed 5-cone. On the assumption that the scalar is constant the 5-geodesic equation yields the Lorentz equation of motion for a charged particle. Intrinsic mass and intrinsic charge are introduced as new particle parameters. Mass and charge formulas are proposed.     

A note on the solution of a spinor equation

An equation of spinor algebra, which is specified by two positive integers,M andN, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree isN}-1. The case in whichN=1 reduces to a well-known result of spinor algebra. The caseM=N=4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.     

Cosmic spinor fields and the early universe

The energy production through expansion of the universe is studied for the Dirac spinor field in all three types of Robertson-Walker universes. Only in the open case is the matter production unlimited (closed universe: limited; flat universe: impossible). The physical properties of the cosmological solutions to the Dirac equation over any RW background are studied in detail.