Hamiltonian field theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F02%3A00000084" target="_blank" >RIV/47813059:19610/02:00000084 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Hamiltonian field theory

Popis výsledku v původním jazyce

In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential syste

Název v anglickém jazyce

Hamiltonian field theory

Popis výsledku anglicky

In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential syste

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F00%2F0724" target="_blank" >GA201/00/0724: Geometrická analýza</a><br>

Návaznosti

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

Rok uplatnění

2002

Kód důvěrnosti údajů

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

Název periodika

Journal of Geometry and Physics

ISSN

ISSN0393-0440

e-ISSN

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Svazek periodika

43

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

IT - Italská republika

Počet stran výsledku

40

Strana od-do

93-132

Kód UT WoS článku

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EID výsledku v databázi Scopus

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