arXiv subjects

Maria Tashkova

Publications and source records attributed to Maria Tashkova.

14 recordsLinked to original sources

arXiv2016

On the Pre-metric Formulation and Nonlinearization of Charge-free Electrodynamics

This paper presents a coordinate free pre-metric formulation of charge free Maxwell-Minkowski electrodynamics, and of the developed by the authors non-linear Extended Electrodynamics. First we introduce some formal relations from multilinear algebra and differential geometry to be used further. Then we recall and appropriately modify the existing pre-metric formulation of linear charge free electrodynamics in pre-relativistic and relativistic forms as preparation to turn to corresponding pre-metric nonlinearization. After some preliminary examples and notes on nonlinearization, we motivate our view for existence and explicit formulation of time stable subsystems of the physical field objects considered. Section 5 presents the formal results of our approach on the pre-metric nonlinear formulations in static case, in time-dependent case, and in space-time formulation. In the Conclusion we give our general view on "why and how to nonlinearize". The Appendix gives a possible formal extension of our aproach to many subsystem field objects.

math-ph↗

arXiv2015

Electromagnetic field objects in terms of Balance of Geometric flows

This paper reviews our physical motivation for choosing appropriate formal presentation of electromagnetic field objects (EMFO). Our view is based on the understanding that EMFO are spatially finite entities carrying internal dynamical structure, so, their available integral time stability should be represented by appropriate adaptation of their internal dynamical structure to corresponding local stress-energy-momentum balance relations with other physical objects. This adaptation process has two aspects: internal and external. Clearly, finding adequate internal dynamical structure giving appropriate integral characteristics of the object, will bring also appropriate behavior of EMFO as a whole. Therefore, the internal local stress-energy-momentum balance among the subsystems of EMFO should formally be presented by appropriately defined tensor-field quantities, which are meant to suggest a dynamical understanding of the abilities of EMFO to successfully communicate with all the rest physical world.

physics.gen-ph↗

arXiv2015

Geometric View on Photon-like Objects

This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange relations and making use of modern differential geometry. In particular, we interpret dynamically Frobenius integrability theory of distributions on manifolds through an appropriate $φ$-extension along $p$-vector fields of the classical Lie derivative, and give interaction interpretation of the nonintegrability of subdistributions of an integrable distribution recognizing physically these subdistributions as time-stable subsystems of the field object considered and formally presented by the integrable distribution. The space-time propagation of our photon-like object is, of course, along appropriate symmetry of the representing distribution.

math-ph↗

arXiv2014

Relativistic Strain and Electromagnetic Photon-Like Objects

This paper aims to relate some properties of photon-like objects, considered as spatially finite time-stable physical entities with dynamical structure, to well defined properties of the corresponding electromagnetic strains defined as Lie derivatives of the Minkowski (pseudo)metric with respect to the eigen vector fields of the Maxwell-Minkowski stress-energy-momentum tensor. First we recall the geometric sense of the concept of strain, then we introduce and discuss the notion for photon-like objects (PhLO). We compute then the strains along the eigen vectors of the stress-energy-momentum tensor $T_μ^ν$ and establish important correspondences with the divergence terms of $T_μ^ν$ and the terms determining some internal energy-momentum exchange between the two recognizable component-fields $F$ and $*F$ of a vacuum electromagnetic field. The role of appropriately defined Frobenius curvature is also discussed and emphasized. Finally, equations of motion and interesting PhLO-solutions are given.

math-ph↗

arXiv2014

A nonlinear prerelativistic approach to mathematical representation of vacuum electromagnetism

This paper presents an alternative prerelativistic approach to the vacuum case of classical electrodynamics represented by vacuum Maxwell equations. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature and the physical relations represented by them should be directly verifiable at least in principle, so they must represent local energy-momentum balance relations.

hep-th↗

arXiv2014

A nonlinear relativistic approach to mathematical representation of vacuum electromagnetism based on extended Lie derivative

This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature. So, they must represent local energy-momentum balance relations. Formally, the new equations are in terms of appropriately extended Lie derivative of $\mathbb{R}^2$-valued differential 2-form along a $\mathbb{R}^2$-valued 2-vector on Minkowski space-time.

hep-th↗

arXiv2009

From Maxwell Stresses to Photon-like Objects through Curvature Geometrisation of Physical Interaction

This paper aims to review our recent results on exploring the capabilities of non-quantum field theory as a possible tool for describing single photon-like objects, considered as massless time-stable spatially finite physical entities with compatible translational-rotational dynamical structure. The main idea is to interpret the local physical interaction as available Frobenius curvature. It consists of five chapters and includes 22 sections and subsections.

math-ph↗

arXiv2008

Nonlinear Connections and Description of Photon-like Objects

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures as generators of measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description of such objects in these terms is given.

math-ph↗

arXiv2008

Frobenius Curvature, Electromagnetic Strain and Description of Photon-like Objects

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems and electromagnetic strain quantities. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures and correspondingly directed strains as measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description (including lagrangian) of such objects in these terms is given.

hep-th↗

arXiv2007

From Maxwell Stresses to Nonlinear Field Equations

This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic terms. The new equations include all Maxwell solutions plus new ones, among which one may find time-stable and spatially finite ones with photon-like properties and behavior.

physics.class-ph↗

arXiv2005

Integrability-Nonintegrability Structures and Individual Photons' Description as Finite Field Objects

This paper presents an attempt to come to a natural field model of individual photons considered as finite entities and propagating along some distinguished direction in space in a consistent translational-rotational manner. The starting assumption reflects their most trustful property to propagate translationally in a uniform way along straight lines. The model gives correct energy-momentum characteristics and connects the rotational characteristics of photons with corresponding nonintegrability (or curvature) of some 2-dimensional distributions (or Pfaff systems) on $\mathbb{R}^4$. It is obtained that the curvature is proportional to the corresponding energy-density. The field equations are obtained through a Lagrangian and they express a consistency condition between photon's translational and rotational propagation properties. The energy tensor is deduced directly from the equations since the corresponding Hilbert energy-tensor becomes zero on the solutions. Planck's formula $E=hν$ is naturally obtained as an integral translational-rotational consistency relation.

hep-th↗

arXiv2005

Extended Electrodynamics: A Brief Review

This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out in relativistic terms in Minkowski space-time. The non-linear vacuum solutions are considered and fully described. It is specially pointed out that solitary waves with various, in fact arbitrary, spatial structure and photon-like propagation properties exist. The {\it null} character of all non-linear vacuum solutions is established and extensively used further. Coordinate-free definitions are given to the important quantities {\it amplitude} and {\it phase}. The new quantity, named {\it scale factor}, is introduced and used as a criterion for availability of rotational component of propagation of some of the nonlinear, i.e. nonmaxwellian, vacuum solutions. The group structure properties of the nonlinear vacuum solutions are analyzed in some detail, showing explicitly the connection of the vacuum solutions with some complex valued functions. Connection-curvature interpretations are given and a special attention is paid to the curvature interpretation of the intrinsic rotational (spin) properties of some of the nonlinear solutions. Several approaches to coordinate-free local description and computation of the integral spin momentum are considered. Finally, a large family of nonvacuum spatial soliton-like solutions is explicitly written down, and a procedure to get (3+1) versions of the known (1+1) soliton solutions is obtained.

hep-th↗

arXiv2002

Parallel Objects and Field Equations

This paper considers a generalization of the existing concept of parallel (with respect to a given connection) geometric objects and its possible usage as a suggesting rule in searching for adequate field equations in theoretical physics. The generalization tries to represent mathematically the two-sided nature of the physical objects, the {\it change} and the {\it conservation}. The physical objects are presented mathematically by sections $Ψ$ of vector bundles, the admissible changes $DΨ$ are described as a rsult of the action of appropriate differential operators $D$ on these sections, and the conservation propertieis are accounted for by the requirement that suitable projections of $DΨ$ on $Ψ$ and on other appropriate sections must be zero. It is shown that the most important equations of theoretical physics obey this rule. Extended forms of Maxwell and Yang-Mills equations are also considered.

math-ph↗

arXiv2002

On the Structure of the Nonlinear Vacuum Solutions in Extended Electrodynamics

In this paper, in the frame of Extended Electrodynamics (EED), we study some of the consequences that can be obtained from the introduced and used by Maxwell equations complex structure \mathcal{J} in the space of 2-forms on \mathbb{R}^4, and also used in EED. First we give the vacuum EED equations with some comments. Then we recall some facts about the invariance group $G$ (with Lie algebra \mathcal{G}) of the standard complex structure $J$ in \mathbb{R}^2. After defining and briefly studying a representation of $G$ in the space of 2-forms on \mathbb{R}^4 and the joint action of $G$ in the space of \mathcal{G}-valued 2-forms on \mathbb{R}^4 we consider its connection with the vacuum solutions of EED. Finally we consider the case with point dependent group parameters and show that the set of the nonlinear vacuum EED solutions is a disjoint union of orbits of the $G$-action, noting some similarities with the quantim mechanical eigen picture and with the QFT creation and anihilation operators.

hep-th↗