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  • $\begingroup$ The systematic approach was first described by Dirac in "Lectures on Quantum Mechanics". For a more recent and comprehensive treatment of the subject have a look at "Quantization of Gauge Systems" by Henneaux and Teitelboim. $\endgroup$
    – Phoenix87
    Commented Sep 4, 2016 at 20:12
  • $\begingroup$ This is covered in detail in Chapters 2 and 5 in Weinberg I. $\endgroup$ Commented Sep 4, 2016 at 21:18
  • $\begingroup$ Generally an equation would remove a degree of freedom, because either it fixes it as in $\mathbf{A}^0=0$ or it expressed one degree of freedom in terms of the others. $\endgroup$ Commented Sep 6, 2016 at 4:13