Notes on Lagrangean and Hamiltonian Symmetries

Abstract

The Hamiltonization of local symmetries of the form $δq^A = \ea{R_a}^A(q,\dot q)$ or $δq^A = \dot\ea{R_a}^A (q,\dot q)$ for arbitrary Lagrangean model $L(q^A,{\dot{q}}^A)$ is considered. We show as the initial symmetries are transformed in the transition from $L$ to first order action, and then to the Hamiltonian action $S_H=\int \mathrm{d}\tau (p_A{\dot{q}}^A-H_0-v^{\alpha }{\Phi }_{\alpha })$, where ${\Phi }_{\alpha }$ are the all (first and second class) primary constraints. An exact formulae for local symmetries of $S_H$ in terms of the initial generators ${R_a}^A$ and all primary constraints ${\Phi }_{\alpha }$ are obtained.

7 pages, LaTeX