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We propose a systematic procedure that solves the Dirac bracket commutators.The method is based on the Gauge Unfixing formalism, a procedure that convertssecond class systems into first class ones without the enlargement of theoriginal phase space variables. We verify that the gauge invariant variablessatisfy the Dirac bracket when we strongly impose the discarded second classconstraint. Thus, we can derive physical operators that satisfy the Diraccommutators. In order to illustrate our procedure, three second classconstrained systems are considered. Firstly, the free particle on the twodimensional sphere is treated. The second case considered is the noncommutativefree particle and the third is the doubly special relativity particle.

The Gauge Unfixing Formalism and the Solutions of the Dirac Bracket Commutators