Superconducting phase transition and gauge dependence

The gauge dependence of the renormalization group functions of the Ginzburg -Landau model is investigated. The analysis is done by means of the Ward-Ta kahashi identities. After defining the local superconducting order paramete r, it is shown that its exponent beta is in fact gauge independent. This ha ppens because in d =3 the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gaug e choice is possible. The analysis is done in both the context of the epsil on expansion and in the fixed dimension approach. It is pointed out the dif ferences that arise in both of these approaches concerning the gauge depend ence. [S0163-1829(99)10141-3].