Hamiltonian field theory revisited: A geometric approach to regularity

Kód výsledku v IS VaVaI

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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 revisited: A geometric approach to regularity

Popis výsledku v původním jazyce

A reformulation and generalization of basic concepts such as Hamiltonian system, Hamilton equations, regularity, and Legendre transformation for variational systems on fibered manifolds, is presented. The theory is based on the concept of Lepagean (n+1)-form (where n is the dimension of the base manifold). Contrary to the standard approach, where Hamiltonian theory is related to a single Lagrangian, here a Hamiltonian system is associated with an Euler-Lagrange form, i.e., with the class of all equivalent Lagrangians. Hamilton equations are introduced to be equations for integral sections of an exterior differential system. Relations between extremals and solutions of Hamilton equations are studied in detail. New regularity conditions and Legendre transformation formulas are found a procedure of regularization of variational problems is proposed.

Název v anglickém jazyce

Hamiltonian field theory revisited: A geometric approach to regularity

Popis výsledku anglicky

A reformulation and generalization of basic concepts such as Hamiltonian system, Hamilton equations, regularity, and Legendre transformation for variational systems on fibered manifolds, is presented. The theory is based on the concept of Lepagean (n+1)-form (where n is the dimension of the base manifold). Contrary to the standard approach, where Hamiltonian theory is related to a single Lagrangian, here a Hamiltonian system is associated with an Euler-Lagrange form, i.e., with the class of all equivalent Lagrangians. Hamilton equations are introduced to be equations for integral sections of an exterior differential system. Relations between extremals and solutions of Hamilton equations are studied in detail. New regularity conditions and Legendre transformation formulas are found a procedure of regularization of variational problems is proposed.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2001

Kód důvěrnosti údajů

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

Název statě ve sborníku

Steps in Differential Geometry

ISBN

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ISSN

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e-ISSN

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Počet stran výsledku

21

Strana od-do

187-207

Název nakladatele

Debrecen University

Místo vydání

Debrecen

Místo konání akce

Debrecen

Datum konání akce

1. 1. 2000

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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