Nonequivalent representations of canonical commutation relations in quantum mechanics: The case of the Aharonov-Bohm effect

We stress the role of nonequivalent representations of the canonical commutation relations in quantum mechanics. Such representations occur when the space accessible to the system is not simply connected. An example is the magnetic Aharonov-Bohm effect, which can be interpreted in terms of nonequivalent representations, without explicitly invoking the vector potential in the region accessible to the electrons. (c) 2007 American Association of Physics Teachers