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I have recently been reading Dirac's book on Canonical Quantization of gauge theories, and I have a few questions:

So in the quantization procedure we need to identify all the constraints in the theory. Once this has been done (if we are dealing with a gauge theory) we need to check that all constraints are first class, i.e. that all constraints commute with each other, correct?

Now given that all the constraints commute we deduce that the constraints are satisfied we can be sure that the evolution in the hamiltonian system is equivalent to the evolution in the lagrangian theory i.e. that there equations of motion agree, correct?

Now when studying the Lagrangian theory we can see what are the gauge transformations take for example EM the gauge transformation is just:

[tex]A_\mu(x) \rightarrow A_\mu' = A_\mu(x) +\partial_\mu \theta(x)[/tex]

To understand this in the canonical picture is where I have trouble, its something like the Lie algebra of the constraints generate gauge transformation but how can I see this?

thanks in advance

M