A Dynamical Approach to Gauge Fixing

We study gauge fixing in the generalized Gupta-Bleuler quantization. In this method physical states are defined to be simultaneous null eigenstates of a set of quantum invariants. We apply the method to a solvable model proposed by Friedberg, Lee, Pang and Ren and show that no Gribov-type copies appears by construction. Gauge fixing is significant in quantization of gauge theories. Gribov ambiguities and specially Gribov-type copies [1] have been a challenge for standard methods of quantization. There are some methods to avoid Gribov ambiguities. For example Gribov proposed to restrict field configurations only to those with positive Faddeev-Popov determinant. Recently Klauder [2] has formulated a new method of quantization based on projection operators into gauge invariant states that avoids any gauge fixing procedure and consequently Gribov ambiguities. In this article we propose an alternative approach to this problem. Using the concept of quantum invariants [3], we show that one can avoid Gribov ambiguities by quantizing the whole phase space and then determining the physical (reduced) Hilbert space instead of constructing the Hilbert space based on the reduced phase space [4]. Considering a gauge model given by a Hamiltonian H(q, p) and a set of first class constraints, there exist a generator of gauge transformation that satisfies the following conditions [5, 6], {G, φμ}|M0 = 0, ∗e-mail: [email protected]