Eur. Phys. J. C (2009) 61: 141-183
https://doi.org/10.1140/epjc/s10052-009-0973-7

Review

Symmetries and dynamics in constrained systems

¹ Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 6083 du CNRS, Fédération Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200, Tours, France
² Department of Physics, Sogang University, Seoul, 121-742, South Korea

^* e-mail: park@sogang.ac.kr

Received: 22 October 2008
Published online: 21 March 2009

Abstract

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total Hamiltonian systems. In particular, in analogy to total Hamiltonians, we introduce the notion of total Noether charges. Grassmannian degrees of freedom are also addressed in detail.