arXiv subjects

Friedrich W. Hehl

Publications and source records attributed to Friedrich W. Hehl.

At least 73 records · Page 4Linked to original sources

arXiv2005

Axiomatics of classical electrodynamics and its relation to gauge field theory

We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.

physics.class-ph↗

arXiv2005

Measuring a piecewise constant axion field in classical electrodynamics

In order to settle the problem of the "Post constraint" in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the wave propagation in a homogeneous medium, we show that the reflection and transmission of a wave at an interface between the two media is sensitive to the difference of the axion values. This observation can be used to determine experimentally the axion piece in matter despite the fact that a constant axion value does not contribute to the Maxwell equations.

physics.optics↗

arXiv2005

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

We show that the Einstein-aether theory of Jacobson and Mattingly (J&M) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG). We achieve this by relating the aether vector field of J&M to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime. Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.

gr-qc↗

arXiv2004

Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics

We consider premetric electrodynamics with a local and linear constitutive law for the vacuum. Within this framework, we find quartic Fresnel wave surfaces for the propagation of light. If we require vanishing birefringence in vacuum, then a Riemannian light cone is implied. No proper Finslerian structure can occur. This is generalized to dynamical equations of any order.

gr-qc↗

arXiv2004

Linear media in classical electrodynamics and the Post constraint

The Maxwell equations are formulated in a generally covariant and metric-free way in 1+3 and subsequently in 4 dimensions. For this purpose, we use the excitations $\cal D$, $\cal H$ and the field strengths $E,B$. A local and linear constitutive law between excitations and field strengths is assumed, with a constitutive tensor $χ^{ijkl}=-χ^{jikl}=-χ^{ijlk}$ of 36 components. The properties of this tensor are discussed. In particular, we address the validity of the Post constraint, a subject that is very much under discussion. In this connection, the Tellegen gyrator, the axion field, and the ``perfect electromagnetic conductor'' of Lindell & Sihvola are compared with each other.

physics.class-ph↗

arXiv2004

Dimensions and Units in Electrodynamics

We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwell's equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call {\em premetric classical electrodynamics.} This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of {\sl L.B. Okun} which he had presented at a recent conference.

physics.class-ph↗

arXiv2004

To consider the electromagnetic field as fundamental, and the metric only as a subsidiary field

In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant and metric-independent way. The electromagnetic field is then given in terms of the excitation $H=(H,D)$ and the field strength $F=(E,B)$. Additionally, a local and linear ``spacetime relation'' is assumed between $H$ and $F$, namely $H \sim κF$, with the constitutive tensor $κ$. The propagation is studied of electromagnetic wave fronts (surfaces of discontinuity) with a method of Hadamard. We find a generalized Fresnel equation that is quartic in the wave covector of the wave front. We discuss under which conditions the waves propagate along the light cone. Thereby we derive the metric of spacetime, up to a conformal factor, by purely electromagnetic methods.

physics.class-ph↗

arXiv2004

Electric/magnetic reciprocity in premetric electrodynamics with and without magnetic charge, and the complex electromagnetic field

We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux conservation (Axiom 3) have to be generalized. Electric/magnetic reciprocity constitutes a guiding principle for this undertaking. The extension of the axioms can be implemented at a premetric stage, i.e., when metric and connection of spacetime don't play a role. Complex Riemann-Silberstein fields of the form $(E\pm i {\cal H},{\cal D}\pm i B)$ have a natural place in the theory, independent of the Hodge duality mapping defined by any particular metric.

physics.class-ph↗

arXiv2004

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

We formulate a premetric version of classical electrodynamics in terms of the excitation H and the field strength F. A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday's law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.

gr-qc↗

arXiv2003

Is the Quantum Hall Effect influenced by the gravitational field?

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the realm of (1 + 2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent (`topological'). This suggests that it does not couple to $\mathbf{g}(x)$. We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.

cond-mat↗

arXiv2003

Maxwell's field coupled nonminimally to quadratic torsion: Induced axion field and birefringence of the vacuum

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^α$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}

gr-qc↗

arXiv2003

Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion

In (1+2)-dimensional Poincaré gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\em translational} and {\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {\em Cartan's} (3-dimensional) {\em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque.

gr-qc↗

arXiv2003

Torsion nonminimally coupled to the electromagnetic field and birefringence

In conventional Maxwell--Lorentz electrodynamics, the propagation of light is influenced by the metric, not, however, by the possible presence of a torsion T. Still the light can feel torsion if the latter is coupled nonminimally to the electromagnetic field F by means of a supplementary Lagrangian of the type l^2 T^2 F^2 (l = coupling constant). Recently Preuss suggested a specific nonminimal term of this nature. We evaluate the spacetime relation of Preuss in the background of a general O(3)-symmetric torsion field and prove by specifying the optical metric of spacetime that this can yield birefringence in vacuum. Moreover, we show that the nonminimally coupled homogeneous and isotropic torsion field in a Friedmann cosmos affects the speed of light.

gr-qc↗

arXiv2003

Electromagnetic energy-momentum and forces in matter

We discuss the electromagnetic energy-momentum distribution and the mechanical forces of the electromagnetic field in material media. There is a long-standing controversy on these notions. The Minkowski and the Abraham energy-momentum tensors are the most well-known ones. We propose a solution of this problem which appears to be natural and self-consistent from both a theoretical and an experimental point of view.

physics.class-ph↗

arXiv2002

The Cauchy Relations in Linear Elasticity Theory

In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.

cond-mat↗

arXiv2002

Light propagation in generally covariant electrodynamics and the Fresnel equation

Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation $H=({\cal D},{\cal H})$ and the field strength $F=(E,B)$. We study the propagation of electromagnetic waves in such a spacetime by Hadamard's method and arrive, with the constitutive tensor density $κ\sim\partial H/\partial F$, at a Fresnel equation which is algebraic of 4th order in the wave covector. We determine how the different pieces of $κ$, in particular the axion and the skewon pieces, affect the propagation of light.

gr-qc↗

arXiv2002

On a possible new type of a T odd skewon field linked to electromagnetism

In the framework of generally covariant (pre-metric) electrodynamics (``charge & flux electrodynamics''), the Maxwell equations can be formulated in terms of the electromagnetic excitation $H=({\cal D}, {\cal H})$ and the field strength $F=(E,B)$. If the spacetime relation linking $H$ and $F$ is assumed to be {\em linear}, the electromagnetic properties of (vacuum) spacetime are encoded into 36 components of the vacuum constitutive tensor density $χ$. We study the propagation of electromagnetic waves and find that the metric of spacetime emerges eventually from the principal part $^{(1)}χ$ of $χ$ (20 independent components). In this article, we concentrate on the remaining skewon part $^{(2)}χ$ (15 components) and the axion part $^{(3)}χ$ (1 component). The skewon part, as we'll show for the first time, can be represented by a 2nd rank traceless tensor $\not S_i{}^j$. By means of the Fresnel equation, we discuss how this tensor disturbs the light cones. Accordingly, this is a mechanism for violating Lorentz invariance and time symmetry. In contrast, the (abelian) axion part $^{(3)}χ$ does {\em not} interfere with the light cones.

gr-qc↗

arXiv2002

Generally covariant Fresnel equation and the emergence of the light cone structure in linear pre-metric electrodynamics

We study the {\em propagation of electromagnetic waves} in a spacetime devoid of a metric but equipped with a {\em linear} electromagnetic spacetime relation $H\simχ\cdot F$. Here $H$ is the electromagnetic excitation $({\cal D},{\cal H})$ and $F$ the field strength $(E,B)$, whereas $χ$ (36 independent components) characterizes the electromagnetic permittivity/permeability of spacetime. We derive analytically the corresponding Fresnel equation and show that it is always quartic in the wave covectors. We study the `Fresnel tensor density' ${\cal G}^{ijkl}$ as (cubic) function of $χ$ and identify the leading part of $χ$ (20 components) as indispensable for light propagation. Upon requiring electric/magnetic reciprocity of the spacetime relation, the leading part of $χ$ induces the {\em light cone} structure of spacetime (9 components), i.e., the spacetime metric up to a function. The possible existence of an Abelian {\em axion} field (1 component of $χ$) and/or of a {\em skewon} field (15 components) and their effect on light propagation is discussed in some detail. The newly introduced skewon field is expected to be T-odd and related to dissipation.

gr-qc↗