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.

Basic information

• 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

• 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

Abstract

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)

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

• 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