Abstract
We demonstrate the power of using nonholonomic fields in various physical systems. Functional integrals over nonholonomic fields describe the statistical mechanics of defects in crystals and of vortices in superflu-ids and superconductors. Nonholonomic distortions of spacetime transform known physical laws in flat space into hitherto unknown laws in spaces with curvature and torsion, thereby leading to a new quantum equivalence principle for the quantum mechanics in such spaces. A gauge structure inherent in nonholonomic fields is exhibited and analyzed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Kleinert, Gauge fields in Condensed Matter,Vol. I: Superfiow and Vortex Lines,Disorder Fields, Phase Transitions, Vol. II: Stresses and Defects, Differential Geometry, Crystal Defects, World Scientific, Singapore, 1989.
H. Kleinert, Lett. Nuovo Cimento 35, 405 (1982). See also the more detailed discussion in Ref. [1], Vol I, Part 2, Section13, where the final disorder theory was derived [see, in particular, Eq. (13.30)].
B.I. Halperin, T.C. Lubensky, and S. Ma, Phys. Rev. Lett. 32, 292 (1972).
M. Kiometzis, H. Kleinert, and A.M.J. Schakel, Phys. Rev. Lett. 73, 1975 (1994).
M. Gabay and A. Kapitulnik, Phys. Rev. Lett. 71, 2138 (1993).
S.-C. Zhang, ibid., 2142 (1993).
M.T. Chen, J.M. Roessler, and J.M. Mochel, J. Low Temp. Phys. 89 125 (1992).
Kleinert, H., Lett. Nuovo Cimento 35 405 (1982).
D. Nelson, Phys. Rev. B 18, 2318 (1978).
D. Nelson and B.I. Halperin, Phys. Rev. B 19, 2457 (1979).
A.P. Young, ibid., 1855 (1979).
D. Nelson, Phys. Rev. B 26 269 (1982).
W. Janke and H. Kleinert, Phys. Lett. A 105, 134 (1984); Phys. Lett. A 114, 255 (1986).
W. Janke and H. Kleinert, Phys. Rev. Lett. 61 2344 (1988).
H. Kleinert, Phys. Lett. A 130 443 (1988).
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics World Scientific Publishing Co., Singapore 1990; extended German edition published by B.I.-Wissenschaftsverlag, Mannheim 1993.
P. Fiziev and H. Kleinert, New Action Principle for Classical Particle Trajectories In Spaces with Torsion, Berlin preprint 1993.
P. Fiziev and H. Kleinert, Action Principle for Euler Equations in Body System, Berlin preprint 1994.
H. Kleinert, Phys. Lett. A 130 (1988).
H. Kleinert and W. Miller, Phys. Rev. Lett. 56, 11 (1986); Phys. Rev. D 38, 1239(1988).
S. Elitzur, Phys. Rev. D 12, 3978 (1975).
P.A.M. Dirac, Principles of Quantum Mechanics, 4th ed., Clarendon, Cambridge 1981, Section80.
J. Schwinger, Phys. Rev. 115, 721 (1959); 127, 324 (1962).
M. Kiometzis and A.M.J. Schakel, Int. J. Mod. Phys. B 7, 4271 (1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kleinert, H. (1995). Theory of Fluctuating Nonholonomic Fields and Applications: Statistical Mechanics of Vortices and Defects and New Physical Laws in Spaces with Curvature and Torsion. In: Davis, AC., Brandenberger, R. (eds) Formation and Interactions of Topological Defects. NATO ASI Series, vol 349. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1883-9_8
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1883-9_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5767-4
Online ISBN: 978-1-4615-1883-9
eBook Packages: Springer Book Archive