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 explicitly broken by the scale of non-commutativity Θ. The effective problem in non-commutative space is analyzed. It is shown that despite the presence of a higher singular potential coming from the leading term of the expansion of the potential to first order in Θ, it can have a self-adjoint extension. The boundary conditions are obtained, which belong to a 1-parameter family and are related to the strength of non-commutativity.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- September 2009
- DOI:
- 10.1088/1751-8113/42/35/355206
- arXiv:
- arXiv:0812.1490
- Bibcode:
- 2009JPhA...42I5206R
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 4 pages, 2 figures, revtex