Hamiltonian dynamics with gauge freedoms revisited

Autor: Guillermo Ruggeri

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Abstract:

Local, finite-dimensional, Hamiltonian dynamics with constraints and gauge freedoms is revisited following a constructive approach. Explicit criteria and algorithms concerning the existence and form of subsidiary conditions, and of generators of both primary and secondary gauge freedoms, are given. Dynamical brackets to represent the general form of evolution equations are identified. Explicit forms for the evolution equations of physical and non physical variables are given and their structure and dynamical meaning analyzed. Dirac’s Conjeture is discussed. A Lie bracket is constructed in terms of which evolution equations exhibit the complete set of physically equivalent trajectories.

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