Aharonov–Bohm Effect and Inequivalent Representations of CCR

Asao Arai

We consider a representation of canonical commutation relations (CCR) appearing in a (non-Abelian) gauge theory on a non-simply connected region in the two-dimensional Euclidean space.A necessary and sufficient condition for the representation to be equivalent to the Schrödinger representation of CCR is given in terms of Wilson loops.A representation inequivalent to the Schrödinger representation gives a mathematical expression for the (non-Abelian) Aharonov-Bohm effect.Some aspects of the Dirac-Weyl operator associated with the representation of CCR are discussed.

Donald H. Kobe

Vladimir D. Skarzhinsky

Arai, A.

We consider a representation of canonical commutation relations (CCR) appear­ing in a (non-Abelian) gauge theory on a non-simply connected region in the two­dimensional Euclidean space. A necessary and sufficient condition for the representa­tion to be equivalent to the Schrodinger representation of CCR is given in terms of Wilson loops. A representation inequivalent to the Schrodinger representation gives a mathematical expression for the (non-Abelian) Aharonov-Bohm effect. Some aspects of the Dirac-Weyl operator associated with the representation of CCR are discussed.

César R. de Oliveira, Renan Gambale Romano

Rathindra Nath Sen

The existence of inequivalent irreducible unitary representations of the CCR suggests that two identical charged bosons may, under suitable conditions, be unable to interact with each other even though their wave functions overlap considerably in space at a fixed time. An experiment is proposed to test this possibility.