Quantization without gauge fixing: avoiding Gribov ambiguities through thephysical projector

The quantization of gauge invariant systems usually proceeds through some g auge fixing procedure of one type or another. Typically for most cases, suc h gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible gauge fixing that the correct dynamical description of the syste m is represented, especially with regards to nonperturbative phenomena. How ever, any gauge fixing procedure whatsoever may be avoided altogether, by u sing rather a recently proposed new approach based on the projection operat or onto physical gauge invariant states only, which is necessarily free of any such issues. These different aspects of gauge invariant systems are exp licitly analysed within a solvable U(1) gauge invariant quantum mechanical model related to the dimensional reduction of Yang-Mills theory.