Symplectic structures related with higher order variational problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F15%3AN0000012" target="_blank" >RIV/47813059:19610/15:N0000012 - isvavai.cz</a>
Result on the web
<a href="http://www.worldscientific.com/doi/abs/10.1142/S021988781550084X" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S021988781550084X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S021988781550084X" target="_blank" >10.1142/S021988781550084X</a>
Alternative languages
Result language
angličtina
Original language name
Symplectic structures related with higher order variational problems
Original language description
In this paper, we derive the symplectic framework for field theories defined by higher order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher order system of partial differential equations to a constrained first-order one, the symplectic structures naturally arising in the dynamics of a first-order Lagrangian theory, and the importance of the Poincare-Cartan form for variational problems, are all well-established facts. However, their adequate combination corresponding to higher order theories is missing in the literature. Here we obtain a consistent and truly finite-dimensional canonical formalism, as well as a higher order version of the Poincare-Cartan form. In our exposition, the rigorous global proofs of the main results are always accompanied by their local coordinate descriptions, indispensable to work out practical examples.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Geometric Methods in Modern Physics
ISSN
0219-8878
e-ISSN
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Volume of the periodical
12
Issue of the periodical within the volume
9
Country of publishing house
SG - SINGAPORE
Number of pages
45
Pages from-to
1-45
UT code for WoS article
000362847100003
EID of the result in the Scopus database
2-s2.0-84943584905