Symplectic structures related with higher order variational problems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Symplectic structures related with higher order variational problems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Symplectic structures related with higher order variational problems

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Geometric Methods in Modern Physics

ISSN

0219-8878

e-ISSN

—

Svazek periodika

12

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

45

Strana od-do

1-45

Kód UT WoS článku

000362847100003

EID výsledku v databázi Scopus

2-s2.0-84943584905