Non-commutativity as a measure of inequivalent quantization
Abstract
We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system is known to be explicitly broken by the scale of non-commutativity . The resulting problem in non-commutative space is analyzed. It is shown that despite the presence of higher singular potential coming from the leading term of the expansion of the potential to first order in , it can have a self-adjoint extensions. The boundary conditions are obtained, belong to a 1-parameter family and related to the strength of non-commutativity.
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