On the Carathéodory Form in Higher-Order Variational Field Theory

On the Carathéodory Form in Higher-Order Variational Field Theory

The Carathéodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrinsic geometric operations applied to the well-known Poincaré–Carta...

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Bibliographic Details
Main Authors: Zbyněk Urban, Jana Volná
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Symmetry
Subjects:
Carathéodory form
Poincaré–Cartan form
Lepage equivalent
fibered manifold
variational field theory
Online Access:https://www.mdpi.com/2073-8994/13/5/800
Description
Summary:The Carathéodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrinsic geometric operations applied to the well-known Poincaré–Cartan form and principal component of Lepage forms, respectively. For second-order theory, our definition coincides with the previous result obtained by Crampin and Saunders in a different way. The Carathéodory equivalent of the Hilbert Lagrangian in general relativity is discussed.
ISSN:2073-8994

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