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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].

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].

Reviewer: Paninjukunnath Achuthan (Madras)

### 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) |

### Keywords:

gravitational theory
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\textit{S. Donev} and \textit{M. Tashkova}, in: Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 8--13, 2007. Sofia: Bulgarian Academy of Sciences. 187--197 (2008; Zbl 1219.83002)

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