arXiv subjects

Yakov Itin

Publications and source records attributed to Yakov Itin.

At least 37 records · Page 2Linked to original sources

arXiv2014

Covariant jump conditions in electromagnetism

A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants.

gr-qc↗

arXiv2013

Skewon no-go theorem

Axion modification of the electrodynamics can be considered as produced by an irreducible part of the constitutive pseudotensor. In this paper, we study the modification of wave propagation produced by the second irreducible part called skewon. We introduce the notions of skewon optic tensor and skewon optic covector. With these devices we prove that in a pseudo-Riemannian manifold endowed with an arbitrary skewon at least one solution of the dispersion relation is spacelike. This means that the skewon generates superluminal wave motion and is thus ruled out on the basis of SR principles.

hep-th↗

arXiv2012

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.

cond-mat.other↗

arXiv2010

Low-dimensional electric charges. Covariant description

A compact and elegant description of the electromagnetic fields in media and in vacuum is attained in the differential forms formalism. This description is explicitly invariant under diffeomorphisms of the spacetime so it is suitable for arbitrary curvilinear coordinates. Moreover, it is independent of the geometry of the underline spacetime. The bulk electric charge and current densities are represented by twisted non-singular differential 3-forms. The charge and current densities with a support on the low dimensional submanifolds (surfaces, strings and points) naturally require singular differential forms. In this paper, we present a covariant metric-free description of the surface, string and point densities. It is shown that a covariant description requires Dirac's delta-forms instead of delta-functions. Covariant metric-free conservation laws for the low-dimensional densities are derived.

math-ph↗

arXiv2010

An electric charge has no screw sense--a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues

Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.

physics.class-ph↗

arXiv2009

Dispersion relation for anisotropic media

The electromagnetic wave propagation in an anisotropic dielectric media with two generic matrices $ε^{ij}$ and $μ^{ij}$ of permittivity and permeability is studied. These matrices are not required to be symmetric, positive definite, and even invertible. In the framework of a metric-free electrodynamics approach, compact tensorial dispersion relation is derived. The resulted formula are useful for a theoretical study of electromagnetic wave propagation in a classical media and in a modern type of media with a generic linear constitutive relation including metamaterials.

physics.class-ph↗

arXiv2009

On light propagation in premetric electrodynamics. Covariant dispersion relation

The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism emerges also when the non-minimal coupling between the electromagnetic tensor and the torsion of Einstein-Cartan gravity is considered. Moreover, the premetric formalism can serve as a general covariant background of the electromagnetic properties of anisotropic media. In the current paper, we study wave propagation in the premetric electrodynamics. We derive a system of characteristic equations corresponded to premetric generalization of the Maxwell equation. This singular system is characterized by the adjoint matrix which turns to be of a very special form -- proportional to a scalar quartic factor. We prove that a necessary condition for existence a non-trivial solution of the characteristic system is expressed by a unique scalar dispersion relation. In the tangential (momentum) space, it determines a fourth order light hypersurface which replaces the ordinary light cone of the standard Maxwell theory. We derive an explicit form of the covariant dispersion relation and establish it'salgebraic and physical origin.

hep-th↗

arXiv2007

Coframe geometry and gravity

The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Maxwell-like system of equations. In the framework of the coframe geometry construction, we propose a geometrical action for the coframe gravity. It is similar to the Einstein-Hilbert action of GR, but the scalar curvature is constructed from the general coframe connection. We show that this geometric Lagrangian is equivalent to the coframe Lagrangian up to a total derivative term. Moreover there is a family of coframe connections which Lagrangian does not include the higher order terms at all. In this case, the equivalence is complete.

gr-qc↗

arXiv2007

Photon propagator for axion electrodynamics

The axion modified electrodynamics is usually used as a model for description of possible violation of Lorentz invariance in field theory. The low-energy manifestation of Lorentz violation can hopefully be observed in experiments with the electromagnetic waves. It justifies the importance of study how a small axion addition can modify the wave propagation. Although a constant axion does not contribute to the dispersion relation at all, even a slowly varying axion field destroys the light cone structure. In this paper, we study the wave propagation in the axion modified electrodynamics in the framework of premetric approach. In an addition to the modified dispersion relation, we derive the axion generalization of the photon propagator in Feynman and Landau gauge. Our consideration is free from the usual restriction of a usual restriction to the constant gradient axion field. It is remarkable that the axion modified propagator is hermitian. Consequently the dissipation effects absent even in the phenomenological model considered here.

hep-th↗

arXiv2007

Wave propagation in axion electrodynamics

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor.We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian.

hep-th↗

arXiv2007

A generalized photon propagator

A covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. A generalized photon propagator is derived. For Maxwell constitutive tensor, the standard light cone structure and the standard Feynman propagator are reinstated.

hep-th↗

arXiv2006

Recent developments in premetric classical electrodynamics

Classical electrodynamics can be based on the conservation laws of electric charge and magnetic flux. Both laws are independent of the metric and the linear connection of spacetime. Within the framework of such a premetric electrodynamics -- provided a local and linear constitutive law of the vacuum is added -- the propagation of electromagnetic waves in the geometric-optics limit can be studied. The wave vectors of the wave fronts obey a quartic extended Fresnel equation. If one forbids birefringence in vacuum, the light cone emerges and Maxwell-Lorentz vacuum electrodynamics can be recovered. If minimal coupling of electrodynamics to gravity is assumed, then only the gravitational potential, i.e., the metric of spacetime, emerges in the constitutive law. We discuss recent results within this general framework.

physics.class-ph↗

arXiv2006

Equations of motion for a (non-linear) scalar field model as derived from the field equations

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for thederivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a nonlinear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the $N$-body problem of the Lorentz invariant field equations.

gr-qc↗

arXiv2006

Maxwell-type behaviour from a geometrical structure

We study which geometric structure can be constructed from the vierbein (frame/coframe) variables and which field models can be related to this geometry. The coframe field models, alternative to GR, are known as viable models for gravity, since they have the Schwarzschild solution. Since the local Lorentz invariance is violated, a physical interpretation of additional six degrees of freedom is required. The geometry of such models is usually given by two different connections -- the Levi-Civita symmetric and metric-compatible connection and the Weitzenbock flat connection. We construct a general family of linear connections of the same type, which includes two connections above as special limiting cases. We show that for dynamical propagation of six additional degrees of freedom it is necessary for the gauge field of infinitesimal transformations (antisymmetric tensor) to satisfy the system of two first order differential equations. This system is similar to the vacuum Maxwell system and even coincides with it on a flat manifold. The corresponding ``Maxwell-compatible connections'' are derived. Alternatively, we derive the same Maxwell-type system as a symmetry conditions of the viable models Lagrangian. Consequently we derive a nontrivial decomposition of the coframe field to the pure metric field plus a dynamical field of infinitesimal Lorentz rotations. Exact spherical symmetric solution for our dynamical field is derived. It is bounded near the Schwarzschild radius. Further off, the solution is close to the Coulomb field.

gr-qc↗

arXiv2005

No-birefringence conditions for spacetime

Within the axiomatic premetric approach to classical electrodynamics, we derive under which covariant conditions the quartic Fresnel surface represents a unique light cone without birefringence in vacuum.

hep-th↗

arXiv2004

Does the coframe geometry can serve as a unification scheme?

The coframe field model is known as a viable model for gravity. The principle problem is an interpretation of six additionaldegrees of freedom. We construct a general family of connections which includes the connections of Levi-Civita and Weitzenböck as the limiting cases. We show that for a special choice of parameters, a subfamily of connections is invariant when the infinitesimal field of transformations (antisymmetric tensor) satisfies the pair of vacuum Maxwell equations -- one for torsion and one for non-metricity. Moreover, the vacuum Maxwell equations turn to be the necessary and sufficient conditions for invariance of the viable coframe action (alternative to GR). Consequently, for the viable models, the coframe field is proved to have the Maxwell-type behavior in addition to the known gravity sector.

gr-qc↗

arXiv2004

Weak field reduction in teleparallel coframe gravity. Vacuum case

The teleparallel coframe gravity may be viewed as a generalization of the standard GR. A coframe (a field of four independent 1-forms) is considered, in this approach, to be a basic dynamical variable. The metric tensor is treated as a secondary structure. The general Lagrangian, quadratic in the first order derivatives of the coframe field is not unique. It involves three dimensionless free parameters. We consider a weak field approximation of the general coframe teleparallel model. In the linear approximation, the field variable, the coframe, is covariantly reduced to the superposition of the symmetric and antisymmetric field. We require this reduction to be preserved on the levels of the Lagrangian, of the field equations and of the conserved currents. This occurs if and only if the pure Yang - Mills type term is removed from the Lagrangian. The absence of this term is known to be necessary and sufficient for the existence of the viable (Schwarzschild) spherical-symmetric solution. Moreover, the same condition guarantees the absence of ghosts and tachyons in particle content of the theory. The condition above is shown recently to be necessary for a well defined Hamiltonian formulation of the model. Here we derive the same condition in the Lagrangian formulation by means of the weak field reduction.

gr-qc↗

arXiv2004

Caroll-Field-Jackiw electrodynamics in the pre-metric framework

We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics reformulated as the ordinary Maxwell theory with an additional special axion field. In this form, the CFJ model appears as a special case of the pre-metric approach recently developed by Hehl and Obukhov. This embedding turns out to be non-trivial. Particularly, the pre-metric energy-momentum tensor does not depend on the axion. This is in contrast to the CFJ energy-momentum tensor which involves the axion addition explicitly. We show that the relation between these two quantities is similar to the correspondence between the Noether conserved tensor and the Hilbert symmetric tensor. As a result the CFJ energy-momentum tensor appears as the unique conserved closure of the pre-metric one. Another problem is in the description of the birefringence effect, which in the pre-metric framework does not depend on the axion. The comparison with the CFJ model shows that the corresponding wave propagation (Fresnel) equation has to be extended by a derivative term, which is non zero for the axion field. In this way, the CFJ birefringence effect is derived in the metric-free approach. Consequently the Lorentz and CPT violating models can be embedded without contradictions in the pre-metric approach to electrodynamics. This correspondence can be useful for both constructions.

hep-th↗