Non-commutativity as a measure of inequivalent quantization

Details Non-commutativity as a measure of inequivalent quantization Non-commutativity as a measure of inequivalent quantization

2008-12-08

arxiv.org/abs/0812.1490v1

J.Phys.A42:355206,2009

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 2 figures, revtex

Scientific paper

10.1088/1751-8113/42/35/355206

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 \Theta. 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 \Theta, 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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