Necessary and Sufficient Conditions of Reducibility of Gauge Degrees of Freedom without Using Gauge Conditions

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Abstract
For dynamical systems described by singular Lagrangian, the conditions under which gauge degrees of freedom can be eliminated by transformations of variables are obtained within the framework of classical dynamics. All the systems whose gauge degrees of freedom are reducible without using gauge conditions may be classified into the following two cases. (i) A weakly reducible case; there exists a canonical transformation by which some of the gauge dependent variables in a Hamiltonian can be separated from other dynamical variables. Hence their gauge degrees of freedom can be completely isolated. (ii) A strongly reducible case; there is a point transformation by which the number of dynamical variables describing a Lagrangian (also a Hamiltonian) of a system can be reducible. Hence the corresponding gauge degrees of freedom are eliminated from the formula. Necessary and sufficient conditions for the reducibility are presented for each case.

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