GEOMETRY OF VARIATIONAL PARTIAL DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F16%3AA1701LHP" target="_blank" >RIV/61988987:17310/16:A1701LHP - 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

GEOMETRY OF VARIATIONAL PARTIAL DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS

Popis výsledku v původním jazyce

This is a survey of Hamiltonian field theory in jet bundles with a particular stress on geometric structures associated with Euler?Lagrange and Hamilton equations. Our approach is based on the concept of Lepage manifold, a fibred manifold endowed with a closed Lepage (n + 1)-form where n is the dimension of the base manifold, which serves as a background for formulation of a covariant Hamilton field theory related to an Euler?Lagrange form (representing variational equations), hence to the class of equivalent Lagrangians. Compared with conventional approaches, dependent upon choice of a particular Lagrangian, this is an important distinction which enables us to enlarge substantially the family of field Lagrangians which possess a canonical multisymplectic Hamiltonian formulation on the affine dual of the jet bundle, and can thus be treated without using the Dirac constraint formalism. Within the Hamiltonian theory on Lepage manifolds, the concepts of regularity and Legendre transformation are revisited and extended, and new formulas for the Hamiltonian and momenta are obtained. In this paper we focus on De Donder?Hamilton equations which arise from ?short? (at most 2-contact) Lepage (n + 1)-forms. To illustrate the results we present regular Lepage manifolds (and the corresponding Hamiltonian formulation) for the Einstein and Maxwell equations.4

Název v anglickém jazyce

GEOMETRY OF VARIATIONAL PARTIAL DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS

Popis výsledku anglicky

This is a survey of Hamiltonian field theory in jet bundles with a particular stress on geometric structures associated with Euler?Lagrange and Hamilton equations. Our approach is based on the concept of Lepage manifold, a fibred manifold endowed with a closed Lepage (n + 1)-form where n is the dimension of the base manifold, which serves as a background for formulation of a covariant Hamilton field theory related to an Euler?Lagrange form (representing variational equations), hence to the class of equivalent Lagrangians. Compared with conventional approaches, dependent upon choice of a particular Lagrangian, this is an important distinction which enables us to enlarge substantially the family of field Lagrangians which possess a canonical multisymplectic Hamiltonian formulation on the affine dual of the jet bundle, and can thus be treated without using the Dirac constraint formalism. Within the Hamiltonian theory on Lepage manifolds, the concepts of regularity and Legendre transformation are revisited and extended, and new formulas for the Hamiltonian and momenta are obtained. In this paper we focus on De Donder?Hamilton equations which arise from ?short? (at most 2-contact) Lepage (n + 1)-forms. To illustrate the results we present regular Lepage manifolds (and the corresponding Hamiltonian formulation) for the Einstein and Maxwell equations.4

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-02476S" target="_blank" >GA14-02476S: Variace, geometrie a fyzika</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

Banach Center Publications

ISBN

978-83-86806-34-8

ISSN

0137-6934

e-ISSN

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Počet stran výsledku

19

Strana od-do

219-237

Název nakladatele

Polish Academy of Sciences, Institute of Mathematics

Místo vydání

Bedlewo

Místo konání akce

Bedlewo

Datum konání akce

10. 5. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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