Variational principle and limit relations in the unified theory of gravitational,electromagnetic, and scalar fields

Within the framework of a special version of unified bimetrical field theory [1], starting from the explicit form of the Lagrangian L, the principal expressions are derived: the field equations, the energy-momentum tensor, the generalized equations of electrodynamics, the conservation laws. Various limiting cases are considered. It is shown that the equations for the electromagnetic field can be obtained as a consequence of the conservation law for the energy-momentum of the unified field.     

Nonlinear Spinor Fields in Bianchi Type-I Spacetime Reexamined

The specific behavior of spinor field in curve space-time with the exception of FRW model almost always gives rise to non-trivial non-diagonal components of the energy-momentum tensor. This non-triviality of non-diagonal components of the energy-momentum tensor imposes some severe restrictions either on the spinor field or on the metric functions. In this paper within the scope of an anisotropic Bianchi type-I Universe we study the role of spinor field in the evolution of the Universe. It is found that there exist two possibilities. In one scenario the initially anisotropic Universe evolves into an isotropic one asymptotically, but in this case the spinor field itself undergoes some severe restrictions. In the second scenario the isotropization takes places almost at the beginning of the process.     

Thick brane solutions supported by two spinor fields

Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane is also considered.     

Polarization of vacuum of quantum fields in the Aaronov-Bohm external field. II

A spinor field interacting with the Aaronov-Bohm external field is examined. Analytical expressions for the vacuum average components of the energy-momentum tensor are derived. Dependences of the components of energymomentum tensor of the spinor field in the vacuum state on the distance and field strength are investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–8, April, 2006.     

The Energy-Momentum Tensor for Electromagnetic Interactions

We compute the energy tensor and the energy-momentum tensor for electrodynamics coupled to the current of a charged scalar field and for electrodynamics coupled tothe current of a Dirac spinor field, without using the equations of motion.     

Gauge Fields in General Parametrical Approach and Their Finslerian Reduction

The covariance principle of general relativity is extended to internal space. Associated gauge fields and tensors are systematically described, whereupon the variational principle is set up for all gauge fields by applying a Palatini-type method, thereby giving rise to an attractive self-contained theory in which the Einstein equations are intrinsically synthesized with the generalized Yang-Mills equations. General gauge-covariant physical field equations are formulated, showing that currents, external + internal spin tensors, and energy-momentum tensors can be introduced unambiguously under these general conditions and that the associated conservation laws can be derived. The electromagnetic field finds its gauge-geometric origin as the gauge field related to internal densities. To be operative with the tensor indices of external and internal types, this general theory must be bimetric. The assumptions that the gauge-covariant derivatives of metric tensors should vanish simplify the theory to the level of a Finslerian gauge approach.     

A new derivation for the field of a time-varying charge in Einstein's theory

A fundamental problem in general relativity is the determination of the field produced by a source configuration consisting of a time-varying charge. By employing a generalized form for the electromagnetic energy-momentum tensor, it is possible to obtain an exact solution of the Einstein field equations for this distribution, without postulating a null fluid.     

Clebsch representations and energy-momentum of the classical electromagnetic and gravitational fields

By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities.     

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.     

Spinor Representations of and Quantum Boson-Fermion Correspondence

This is an extension of quantum spinor construction in [DF2]. We define quantum affine Clifford algebras based on the tensor product of a finite dimensional representation and an infinite highest weight representation of and the solutions of q-KZ equations, construct quantum spinor representations of and explain classical and quantum boson-fermion correspondence. Received: 22 November 1995 / Accepted: 21 July 1998     

Covariant construction of the symmetric energy-momentum tensor of vector and spinor fields in an orthogonal frame of reference

A covariant method is devised to construct the symmetric energy-momentum tensor for vector fields in an orthogonal frame of reference. The method is then used to construct the symmetric energy-momentum tensor for spinor fields. Kazan’ University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1997.     

Vacuum expectation values of the energy-momentum tensor in two dimensions

A general form of the vacuum expectation values of the components of the energy-momentum tensor is derived in the case of static two-dimensional spacetime. Conditions for the regularity of the energy-momentum tensor are set. A generalized formula for the black hole temperature originally found by Hawking is given. The regularity of the energy-momentum tensor in the presence of more than one horizon is investigated.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland.     

Nonlinear Spinor Fields in Bianchi type-III Spacetime

Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In this case the spacetime remains locally rotationally symmetric and anisotropic all the time. It is found that depending on the sign of nonlinearity the models allows both accelerated and oscillatory modes of expansion. The non-diagonal components of energy-momentum tensor though impose some restrictions on metric functions and components of spinor field, unlike Bianchi type I, V and V I ₀ cases, they do not lead to vanishing mass and nonlinear terms of the spinor field.     

Spinor fields in Bianchi type-I universe

A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.     

Some remarks on the energy-momentum tensor in general relativity

In general relativity, the energy-momentum tensor of a classical tensor field can be constructed by varying the action of the field with respect to the background metric. This paper suggests an alternative interpretation of the construction which also makes sense for spinor fields, and which gives some insight into the locality of energy-momentum operators in generally covariant quantum field theory.     

Two theorems on energy-momentum conservation

The mathematical meaning of the law of conservation of energy-momentum is examined. A distinction is made between the intrinsic properties of the metric tensor (i.e., those properties that are independent of the coordinate system), and the nonintrinsic properties of this tensor (i.e., those properties that depend upon the coordinate system). The covariance of the energy-momentum law is used to demonstrate that if one is given (a) any analytic contravariant energy-momentum tensor density in a given coordinate systemx and (b) an analytic specification of the intrinsic properties of the metric tensor, no matter what these properties may be, one can always choose the nonintrinsic properties of the metric tensor in such manner as to satisfy the law of conservation of energy-momentum in the coordinate systemx and thereby in every coordinate system. This result is proved only in the case where the contravariant components of the energy-momentum tensor density are given. Neither the covariant, nor the mixed energy-momentum tensor densities are considered. Other theorems similar to that described above are also derived. Many of the results obtained are nontrivial even when space-time is flat.     

Space-time in ordered electromagnetic radiation outside a massive plane

The Einstein-Maxwell equations are solved with an energy-momentum tensor corresponding to the field of a standing electromagnetic wave outside a massive plane, in the limit where the test particle is much larger than the wavelength of the electromagnetic field. Physical properties of the solution are discussed.     

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

Quantum effects in cosmological models with singularities

The vacuum expectation values of the energy-momentum tensor of quantized scalar and spinor fields in a de Sitter space of the first kind are calculated. Limiting cases of the obtained exact expressions are considered. It is noted that the de Sitter space is a self-consistent solution of the Einstein equations with allowance for quantum vacuum fluctuations of massless fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 67–70, January, 1981.I thank V. M. Mostepanenko and B. N. Sharapov for numerous helpful discussions.