What is a Gauge Transformation in Quantum Mechanics?

Abstract

In classical theory, a physical state is an equivalence class under gauge transformations. Is the same true in quantum theory? The physical quantum states are the solutions of Dirac's quantum constraint equation. They cannot be constructed as equivalence classes under the ``simple'' gauge transformations generated by the Dirac constraints. However, we show here that they can be constructed as equivalence classes under suitably defined ``complete'' gauge transformations. The complete gauge transformations are generated by the action of the quantum constraints on arbitrary individual components of the state.