Proceedings of the International Conference on Geometry, Integrability and Quantization

Essential Nonlinearity in Field Theory and Continuum Mechanics. Second- and First-order Generally-covariant Models

Ewa E. Rożko and Jan J. Sławianowski

Abstract

Discussed is the problem of the mutual relationship of differentially first-order and second-order field theories and quantum-mechanical concepts. We show that unlike the real history of physics, the theories with algebraically second-order Lagrangians are primary, and in any case more adequate. It is shown that in principle, the primary Schrödinger idea about Lagrangians which are quadratic in derivatives, and leading to second-order differential equations, is not only acceptable, but just it opens some new perspective in field theory. This has to do with using the Lorentz-conformal or rather its universal covering SU(2,2) as a gauge group. This has also some influence on the theory of defects in continua.

Article information

Source
Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2014), 218-241

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815713

Digital Object Identifier
doi:10.7546/giq-15-2014-218-241

Mathematical Reviews number (MathSciNet)
MR3287760

Zentralblatt MATH identifier
1305.81080

Citation

Rożko, Ewa E.; Sławianowski, Jan J. Essential Nonlinearity in Field Theory and Continuum Mechanics. Second- and First-order Generally-covariant Models. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 218--241, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-218-241. https://projecteuclid.org/euclid.pgiq/1436815713


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