Representation of the Variational Sequence by Differential Forms
KRBEK, Michael and Jana MUSILOVÁ. Representation of the Variational Sequence by Differential Forms. Acta Applicandae Mathematicae. Kluwer, 2005, 88 / 2005, No 1, p. 177-199. ISSN 0167-8019. |
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Basic information | |
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Original name | Representation of the Variational Sequence by Differential Forms |
Name in Czech | Reprezentace variační posloupnosti diferenciálními formami |
Authors | KRBEK, Michael (203 Czech Republic, guarantor) and Jana MUSILOVÁ (203 Czech Republic). |
Edition | Acta Applicandae Mathematicae, Kluwer, 2005, 0167-8019. |
Other information | |
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Original language | English |
Type of outcome | Article in a journal |
Field of Study | 10301 Atomic, molecular and chemical physics |
Country of publisher | Netherlands |
Confidentiality degree | is not subject to a state or trade secret |
Impact factor | Impact factor: 0.456 |
RIV identification code | RIV/00216224:14310/05:00012697 |
Organization unit | Faculty of Science |
UT WoS | 000231706600003 |
Keywords (in Czech) | variační posloupnost konečného řádu; diferenciální formy; reprezentace |
Keywords in English | finite order variational sequence; differential forms; representation |
Tags | differential forms, finite order variational sequence, representation |
Tags | International impact, Reviewed |
Changed by | Changed by: prof. RNDr. Jana Musilová, CSc., učo 851. Changed: 23/6/2009 22:37. |
Abstract |
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In the paper the representation of the finite order variational sequence on fibered manifolds in field theory is studied. The representation problem is completely solved by a generalization of the integration by parts procedure using the concept of Lie derivative of forms with respect to vector fields along canonial maps of prolongatios of fibered manifolds. A close relationship between the obtained coordinate invariant representation of the variational sequence and some familiar objects of physics, such as Lagrangians, dynamical forms, Euler-Lagrange mapping and Helmholtz-Sonin mapping is pointed out and illustrated by examples. |
Abstract (in Czech) |
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Článek se zabývá studiem reprezentace variační posloupnosti koneného řádu v teorii pole na fibrovaných varietách. Problém reprezentace je kompletně vyřešen pomocí zobecnění integrace per partes a použitím Lieovy derivace forem podle vektorových polí podél kanonických zobrazení prodloužení fibrovaných variet. Je zdůrazněn vztah mezi získnou souřadnicově invariantní reprezentací variační posloupnosti a známými fyziklními objekty - Lagrangiány, dynamickými formami, Eulerovým-Lagrangeovým zobrazením, Helmholtzovým-Soninovým zobrazením. |
Links | |
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GA201/03/0512, research and development project | Name: Geometrická analýza a její aplikace ve fyzice |
Investor: Czech Science Foundation, Geometric analysis and its applications in physics | |
MSM0021622409, plan (intention) | Name: Matematické struktury a jejich fyzikální aplikace |
Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications |
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