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Nonlinear connections and description of photon-like objects. (English) Zbl 1219.83002

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 187-197 (2008).
The fundamental particle photon and the basic idea of nonlinearity receive attention here. The powerful notion of photon-like objects in nature is introduced and discussed briefly in the paper. The nonlinear connection view on the Frobenius integrability theory on manifolds is considered as a useful frame in which an appropriate description of photon-like objects can be successfully developed and investigated.
The specific sections are: The notion of photon-like objects (PhLO); Nonlinear connections; Back to PhLO; Translational-rotational consistency. There are two figures illustrating certain theoretical examples. Presented are also 3 propositions with proof and discussion. The intricate and interesting relationships between mathematics and physics are spelt out in a very subtle, useful manner. This invites more intensive efforts for establishing further results on the concepts of nonlinearity and the beautiful photon.
For the entire collection see [Zbl 1154.17001].

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C10 Equations of motion in general relativity and gravitational theory
83C50 Electromagnetic fields in general relativity and gravitational theory
83E05 Geometrodynamics and the holographic principle
78A25 Electromagnetic theory (general)
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