Universität zu Köln

Lazar, Markus ORCID: 0000-0002-0849-9112 and Hehl, Friedrich W. ORCID: 0000-0003-2503-4744 (2010). Cartan's Spiral Staircase in Physics and, in Particular, in the Gauge Theory of Dislocations. Found. Phys., 40 (9-10). S. 1298 - 1326. NEW YORK: SPRINGER. ISSN 0015-9018

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Abstract

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 Poincar, 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lazar, Markus UNSPECIFIED orcid.org/0000-0002-0849-9112 UNSPECIFIED Hehl, Friedrich W. UNSPECIFIED orcid.org/0000-0003-2503-4744 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-495557
DOI:	10.1007/s10701-010-9440-4
Journal or Publication Title:	Found. Phys.
Volume:	40
Number:	9-10
Page Range:	S. 1298 - 1326
Date:	2010
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	0015-9018
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FIELD-THEORY; TORSION; DEFECTS; GRAVITY; STRESS; DISCLINATIONS; SPACETIME; TENSOR; SCREW; MODEL Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49555