On energy-momentum and spin/helicity of quark and gluon fields

In special relativity, quantum matter can be classified according to mass-energy and spin. The corresponding field-theoretical notions are the energy-momentum-stress tensor T and the spin angular momentum tensor S. Since each object in physics carries energy and, if fermionic, also spin, the notions of T and S can be spotted in all domains of physics. We discuss the T and S currents in Special Relativity (SR), in General Relativity (GR), and in the Einstein-Cartan theory of gravity (EC). We collect our results in 4 theses: (i) The quark energy-momentum and the quark spin are described correctly by the canonical (Noether) currents T and S, respectively. (ii) The gluon energy-momentum current is described correctly by the (symmetric and gauge invariant) Minkowski type current. Its (Lorentz) spin current vanishes, S = 0. However, it carries helicity of plus or minus one. (iii) GR contradicts thesis (i), but is compatible with thesis (ii). (iv) Within the viable EC-theory, our theses (i) and (ii) are fulfilled and, thus, we favor this gravitational theory.Comment: 10 pages latex. Invited talk delivered at the XV Workshop on High Energy Spin Physics `DSPIN-13' in Dubna, Russia, 08--12 October 201

Axion and dilaton + metric emerge from local and linear electrodynamics

We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincare group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. --- In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density $\chi^{ijkl}= -\chi^{jikl}= -\chi^{ijlk}$ with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in $\chi^{ijkl}$, it can be derived from it. [file CarlBrans80_07.tex]Comment: 21 pages, 2 figures, invited contribution to the Festschrift for Carl Brans' 80th birthday, reference to P. Russer added, comments of Alan Kostelecky taken care o

A remark on an ansatz by M.W. Evans and the so-called Einstein-Cartan-Evans unified field theory

M.W.Evans tried to relate the electromagnetic field strength to the torsion of a Riemann-Cartan spacetime. We show that this ansatz is untenable for at least two reasons: (i) Geometry: Torsion is related to the (external) translation group and cannot be linked to an internal group, like the U(1) group of electrodynamics. (ii) Electrodynamics: The electromagnetic field strength as a 2-form carries 6 independent components, whereas Evans' electromagnetic construct F^\a is a vector-valued 2-form with 24 independent components. This doesn't match. One of these reasons is already enough to disprove the ansatz of Evans.Comment: 6 pages late

A note on post-Riemannian structures of spacetime

A four-dimensional differentiable manifold is given with an arbitrary linear connection $\Gamma_\alpha^\beta=\Gamma_{i\alpha}^\beta dx^i$. Megged has claimed that he can define a metric $G_{\alpha\beta}$ by means of a certain integral equation such that the connection is compatible with the metric. We point out that Megged's implicite definition of his metric $G_{\alpha\beta}$ is equivalent to the assumption of a vanishing nonmetricity. Thus his result turns out to be trivial.Comment: 3 pages, LaTeX, no figures, reply to gr-qc/970606

Fresnel versus Kummer surfaces: geometrical optics in dispersionless linear (meta)materials and vacuum

Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three quantities: the temporal frequency $\omega$, the spatial wave (co)vector $k$, and the polarisation (co)vector $a$. Numerous key properties of a given optical medium are determined by the Fresnel surface, which is the visual counterpart of the equation relating $\omega$ and $k$. For instance, the propagation of electromagnetic waves in a uniaxial crystal, such as calcite, is represented by two light-cones. Kummer, whilst analysing quadratic line complexes as models for light rays in an optical apparatus, discovered in the framework of projective geometry a quartic surface that is linked to the Fresnel one. Given an arbitrary dispersionless linear (meta)material or vacuum, we aim to establish whether the resulting Fresnel surface is equivalent to, or is more general than, a Kummer surface.Comment: Invited lecture at "Electromagnetic Spacetimes", Wolfgang Pauli Institute, Vienna, 19--23 Nov 201

Computer algebra in gravity

We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some computer algebra systems and packages relevant to applications in gravitational physics. We conclude by presenting a couple of typical examples.Comment: 10 pages, LaTeX2e, hyperref, updated version of an article to appear in: Computer Algebra Handbook. J. Grabmeier, E. Kaltofen, V. Weispfennig, editors (Springer, Berlin 2001/2002

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.Comment: 12 pages late

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.Comment: Elsevier style, 30 pages, 2figures. Accepted for publication in Annals of Physic

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.Comment: 9 pages latex with Kluwer style files, will appear in the J. of Elasticit

Irreducible decompositions of the elasticity tensor under the linear and orthogonal groups and their physical consequences

We study properties of the fourth rank elasticity tensor C within linear elasticity theory. First C is irreducibly decomposed under the linear group into a "Cauchy piece" S (with 15 independent components) and a "non-Cauchy piece" A (with 6 independent components). Subsequently, we turn to the physically relevant orthogonal group, thereby using the metric. We find the finer decomposition of S into pieces with 9+5+1 and of A into those with 5+1 independent components. Some reducible decompositions, discussed earlier by numerous authors, are shown to be inconsistent. --- Several physical consequences are discussed. The Cauchy relations are shown to correspond to A=0. Longitudinal and transverse sound waves are basically related by S and A, respectively.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1208.104