# What is the difference between canonical transformations and gauge transformations?

1. Dec 29, 2011

### zheng89120

I have some ideas of canonical transformation is, but the ideas behind gauge transformation is still eluding me.

2. Dec 30, 2011

### Snicker

Re: What is the difference between canonical transformations and gauge transformation

In short, a canonical transformation is a transformation of the phase space coordinates which maps Hamiltonian flows onto Hamiltonian flows and a gauge transformation defines equivalence classes on field potential functions which leaves "physical fields" invariant.