Position-dependent noncommutativity in quantum mechanics
arXiv:0902.3252 · doi:10.1103/PhysRevD.79.125011
Abstract
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=ω^{ij}(x), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativety.
published version, references added
References in corpus (6)
- Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
- Star products made (somewhat) easier
- Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
- Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
- Dirac Quantization Condition for Monopole in Noncommutative Space-Time
- Born series and unitarity in noncommutative quantum mechanics