Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac–Bergmann Algorithm

The Dirac-Bergmann algorithm is a recipe for converting theory with singular Lagrangian into constrained Hamiltonian system. Constrained systems include gauge theories -- general relativity, electromagnetism, Yang Mills, string theory, etc. elegant but at the same time rather complicated. It consists of large number logical steps linked together by subtle chain reasoning. Examples found in literature are designed to isolate and illustrate just one or two those steps. In this paper I analyze finite-dimensional system that exhibits all major algorithm. includes primary secondary constraints, first second class restrictions on Lagrange multipliers, both physical degrees freedom. This relatively simple provides platform discussing Dirac conjecture, constructing brackets, applying conditions.