Autoparallels From a New Action Principle

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsionComment: Paper in src. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly with Netscape under http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm

An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe

Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur

DISCUSSION ON THE RELATIONSHIP BETWEEN DEEP SEISMIC REFLECTION PATTERNS AND TECTONIC UNITS OF THE EASTERN PART OF THE CENTRAL ASIAN OROGENIC BELT IN NORTHEASTERN CHINA

Division of tectonic units in the eastern part of the Central Asian Orogenic Belt in northeast China has been a major concern and resulted in much fieldwork, but the division of these tectonic units in NE China is still controversial. Although detection of tectonic units in seismic sections is not straightforward, for this meeting, we shall try to relate tectonic units with the crustal and upper mantle structure and deformation derived from a ~2500 km long reflection seismic profile (Figure, red lines) in this area, recently acquired or reprocessed with support of China Geological Survey and the Chinese SinoProbe Project.Division of tectonic units in the eastern part of the Central Asian Orogenic Belt in northeast China has been a major concern and resulted in much fieldwork, but the division of these tectonic units in NE China is still controversial. Although detection of tectonic units in seismic sections is not straightforward, for this meeting, we shall try to relate tectonic units with the crustal and upper mantle structure and deformation derived from a ~2500 km long reflection seismic profile (Figure, red lines) in this area, recently acquired or reprocessed with support of China Geological Survey and the Chinese SinoProbe Project

Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects

We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle, according to which the equations of motion of a point particle in such spaces can be obtained from the Newton equation in euclidean space by means of a nonholonomic mapping. By this principle, the known Langevin equation in euclidean space goes over into the correct Langevin equation in the Cartan space. This, in turn, serves to derive the Kubo and Fokker-Planck equations satisfied by the particle distribution as a function of time in such a space. The theory can be applied to classical diffusion processes in crystals with defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm

Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor

The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct manifestation of inertia. The geometric origin of the torsion force is a closure failure of parallelograms. The torsion force changes the covariant conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm

Volterra Distortions, Spinning Strings, and Cosmic Defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Quantum Gra

Energiestoffwechsel und Serumenzyme

Peer Reviewe

A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended versio

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure