On the Carathéodory Form in Higher-Order Variational Field Theory

Symmetry

Zbyněk Urban¹  Jana Volná¹ 

[1] Department of Mathematics, Faculty of Civil Engineering, VŠB—Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 33 Ostrava, Czech Republic;

关键词: Carathéodory form;    Poincaré–Cartan form;    Lepage equivalent;    fibered manifold;    variational field theory;   

DOI  :  10.3390/sym13050800

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown