A geometrical version of the higher order Hamilton formalism in fibred manifolds
✍ Scribed by Ivan Kolář
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 497 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0393-0440
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✦ Synopsis
It has been clarified recently that an r-th order Lagrangian on a fibred manifold Y X does not determine a unique Poincaré-Carran fonn provided dimX> 1 and r>2, [1], [4], [6], [9], [10]. To make this fact more transparent, we introduced a new operation generalizing the formal exterior differentiation,
[61.In the present paper we deduce in such a way that a unique Poincaré-Cartan form can be determined by means of a simple additional structurea linear symmetric connection F on the base manifold X (or, more generally, by a convenient splitting S). Then we present a suitable geometric definition of a regular r-th order Lagrangian on Y and we prove that any our Poincaré-Cartan form can be used in a geometrical version of the higher order Hamilton formalism.
The starting point for this paper was a lecture presented in the Banach Center at Warsaw during the 1983 Trimester on Mathematical Physics. The author is grateful to Prof. A.Trautman for his interest in the lecture and his comments.