Abstract
The Faddeev and Jackiw procedure for the quantization of constrained gauge systems is used on the analysis of an interacting electron-phonon model including Chern-Simons term. The generalized FJ brackets of this system with first-class constraints are found by removing the singularity in the symplectic matrix. This was done by adding the gauge-fixing term in the symplectic potential. Compared to Dirac’s method, this Faddeev and Jackiw approach is quite straightforward for these systems.
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