## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 8, Number 3 (2004), 565-601.

### Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage-Dedecker versus De Donder-Weyl

Frédéric Hélein and Joseph Kouneiher

#### Abstract

The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the (more usual) De Donder- Weyl (DDW) one. One of the main points is the fact that the Legendre transform in the DDW approach is replaced by a Legendre correspondence in the LP theory (this correspondence behaves differently: ignoring the singularities whenever the Lagrangian is degenerate).

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 8, Number 3 (2004), 565-601.

**Dates**

First available in Project Euclid: 21 October 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1098389091

**Mathematical Reviews number (MathSciNet)**

MR2105190

**Zentralblatt MATH identifier**

1115.70017

#### Citation

Hélein, Frédéric; Kouneiher, Joseph. Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage-Dedecker versus De Donder-Weyl. Adv. Theor. Math. Phys. 8 (2004), no. 3, 565--601. https://projecteuclid.org/euclid.atmp/1098389091