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Bound for Spin-Dependent Non-Commutative Parameter Based on Pauli Equation

 Carlos Alberto Stechhahn de Silva

In this work, we consider a particle moving on a two-dimensional non-commutative plane immersed in a constant magnetic field. The non-commutativity of spatial coordinates, conjugate momentum, and spin variables are supposed to satisfy a "non-standard" Heisenberg algebra. The parameterθ that characterizes the non-commutativity here is not constant and is called "non-commutativity of spin". Using the Pauli equation and perturbation theory, the non-commutativity parameter can be shown, after considering the degeneracy of energy levels, to be bounded by θ<< 10⁻²⁰ cm.