Plane-Symmetric Solitons of Spinor and Scalar Fields

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S= and P=i⁵; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant = _,^,, that becomes linear at 0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.     

Novel Localized Excitations of Nonlinear Coupled Scalar Fields

Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.     

Static Plane-Symmetric Nonlinear Spinor and Scalar Fields in GR

We consider a system of minimally coupled nonlinear spinor and scalar fields within the scope of a plane-symmetric gravitational field. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The change of the sign of the scalar field energy density of the system in question realizes physically if and only if the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. The choice of spinor field nonlinearity leads to the elimination of scalar field contribution to the metric functions, but leaves its contribution to the total energy unaltered. The spinor field is more sensitive to the gravitational field than the scalar field.     

Covariant Quantization of Spinor Fields in a Given Gravitational Field

In coupling gravity with the quantum field theory, unitary transformations, depending on space-time-points, were considered and derivatives were introduced, which imply a nonintegrable parallel transport of the state vectors of Hilbert space [1]. The Dirac equation, built with these generalized derivatives, is quantized in a prescribed classical gravitational field. The quantization can be performed in complete analogy to the usual procedure in Minkowski space, but the quantum state vector becomes path dependent. In carrying out the quantization, two two-component classical spinor fields necessarily occur, which obey Weyl's equation. The considered quantized Dirac equations are also picture-covariant, that is they have the same from in each physical picture, especially in the Heisenberg picture and the Schrödinger picture.     

Acceleration Field of a Universe Modeled as a Mixture of Scalar and Matter Fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely, (a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.     

A Quantum Cosmological Bianchi I Model with Interacting Spinor and Scalar Fields

A Bianchi I model of the Universe filled with interacting nonlinear spinor and scalar fields is studied within quantum geometrodynamics. Three types of interaction are considered: gradient, Yukawa, and axion ones. For massless fermion fields, the variables in the Wheeler – de Witt equation will separate. The solution can be interpreted using a two-component perfect liquid. One component corresponds to a massless scalar field, while the other – to a nonlinear spinor field. The interaction between the spinor and scalar fields can lead to elimination of singularity of the wave function. There is a possibility of existence of a discrete spectrum of the quantum Universe, as well as tunneling from the region with a rigorous equation of state to the region of the de Sitter vacuum.     

Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions

In the framework of Bianchi I (BI) cosmological models a self-consistent system of interacting spinor and scalar fields has been considered. We introduced an interaction function F(I, J) which is an arbitrary function of invariants I and J, generated from the real bilinear forms of the spinor field. Exact self-consistent solutions to the field equations have been obtained for the cosmological model filled with perfect fluid. The initial and the asymptotic behavior of the field functions and of the metric one has been thoroughly studied.     

Dynamics of Solitons in Coupled System of Scalar Fields

The dynamics of interacting solitons of a system of two coupled nonlinear partial differential equations is studied numerically using a finite difference method in bi-dimensional spacetime. Stable, static topological solitons are obtained from an iterative-variational method, and used as initial solutions for the dynamical calculations. Some of the static solutions decay to stable solitons. Some subtle aspects of topological charges for the system under consideration are also discussed.     

Collisional Lifetimes of Elementary Excitations in Two-Dimensional Systems in the Field of a Strong Electromagnetic Wave

A two-dimensional system with two nonequivalent valleys in the field of a strong circularly polarized electromagnetic wave is considered. It is assumed that the optical selection rules for a given polarization of light allow band-to-band transitions only in valleys of one, optically active, type (two-dimensional layer based on transition metal dichalcogenides, gapped graphene, etc.). This leads to the formation of photon-coupled electron–hole pairs, or an “optical insulator” state. It is assumed that the valleys of the second type (optically inactive) are populated with an equilibrium electron gas. The relaxation of elementary excitations in this hybrid system consisting of an electron gas and a gas of electron–hole pairs caused by the Coulomb interaction between the particles is investigated.     

Self-Gravitating String-Like Configurations of Nonlinear Spinor Fields

We consider the problem of the existence of soliton-like self-gravitating cylindrically symmetric configurations of a classical spinor field with the nonlinearity F(S) ( , F is an arbitrary function). Soliton-like configurations should have, by definition, a regular axis of symmetry and a flat or string-like geometry far from the axis (i.e., an asymptotically Minkowskian metric with a possible angular defect). It is shown that these conditions can be fulfilled if F(S) is finite as S and decreases faster than S ² as S 0. The set of field equations is entirely integrated, and some explicit examples are considered. A regularizing role of gravity is discussed.     

Effects of the Gravitational Interaction of a Scalar Field and Magnetic and Electric Vortex Fields

Russian Physics Journal - The combined action of self-gravitating magnetic and electric vortex fields and a self-gravitating scalar field is considered. The properties of wormholes formed as a...     

A Closed Friedmann Universe with a Scalar Field as Source

The evolution is examined of a closed Friedmann universe, the source of which is a classical massive scalar field. Supposing a minimal value a₀ the initial values are chosen in such a way that the solutions are time symmetric. The scale factor passes a maximal value and then decreases to zero (singularity). For special initial values a phase with exponential increasing scale factor exists.     

Spinor Representation of Electromagnetic Fields on Noncommutative Spaces

We apply Campolattaro's spinor representation of the electromagnetic field to noncommutative spaces. The spinor representation of the (self-dual) electromagnetic field on noncommutative spaces is obtained.     

Spinor Wave Equation of Electromagnetic Field

In this paper, we give two spinor wave equations of free electromagnetic field, corresponding to the reducibility and irreducibility representations D ¹⁰+D ⁰¹ and D ¹⁰ of the proper Lorentz group, which are the differential equations of space-time one order. The spinor equations are covariant and are equivalent to Maxwell equations.     

On Some Exponential Potentials for a Cosmological Scalar Field as Quintessence

We present general exact solutions for two classes of exponential potentials in a scalar field model for quintessence. The coupling is minimal and we consider only dust and scalar field. To some extent, it is possible to reproduce experimental results from supernovae.