http://arxiv.org/abs/1702.07598

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.

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L. Lusanna

Mon, 27 Feb 17

23/49

Comments: 38 pages

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