Abstract
We propose a geometric interpretation for the Wess-Zumino (WZ) constraint converting method. This study is done in the context of nonlinearly constrained systems, formulated as gauge theories. A deep unifying concept is revealed connecting the invariant and the noninvariant models disclosing a unique relationship between the WZ gauge orbits with the nonlinear surfaces. Such structures unveil the physical and geometrical meaning of the WZ terms in turning second-class constraints into gauge generators quantities. A simple and practical mapping between gauge and nongauge theories is found, providing a new interpretation for the nonlinear constraint as the natural gauge fixing surface for the gauge theories.
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