On the Carathéodory form in higher-order variational field theory

2021/04/08 by Urban, Zbyněk, Volná, Jana
#58A10 #58A20 #58E30 #70S05 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2104.03609

Abstract

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 intrisic 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.

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