# Dirac-Bergmann Constraints in Physics: Singular Lagrangians, Hamiltonian Constraints and the Second Noether Theorem [CL]

There is a review of the main mathematical properties of system described by singular Lagrangians and requiring Dirac-Bergmann theory of constraints at the Hamiltonian level. The following aspects are discussed:
i) the connection of the rank and eigenvalues of the Hessian matrix in the Euler-Lagrange equations with the chains of first and second class constraints;
ii) the connection of the Noether identities of the second Noether theorem with the Hamiltonian constraints;
iii) the Shanmugadhasan canonical transformation for the identification of the gauge variables and for the search of the Dirac observables, i.e. the quantities invariant under Hamiltonian gauge transformations.
Review paper for a chapter of a future book.

L. Lusanna
Mon, 27 Feb 17
23/49