Spin and Statistics on the GroenewoldMoyal Plane:. PauliForbidden Levels and Transitions
Abstract
The GroenewoldMoyal plane is the algebra { A}_{θ ({ } R}^{d+1}) of functions on &R;^{d+1} with the *product as the multiplication law, and the commutator [hat {x}_{μ ,hat {x}_ν ]} =iθ _{{μ } ν } (μ ,ν =0,1,...,d) between the coordinate functions. Chaichian et al.^{1} and Aschieri et al.^{2} have proved that the Poincaré group acts as automorphisms on { A}_{θ ({ } R}^{d+1}) if the coproduct is deformed. (See also the prior work of Majid,^{3} Oeckl^{4} and Grosse et al.^{5}) In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Ref. 2. In this paper we show that for this new action, the Bose and Fermi commutation relations are deformed as well. Their potential applications to the quantum Hall effect are pointed out. Very striking consequences of these deformations are the occurrence of Pauliforbidden energy levels and transitions. Such new effects are discussed in simple cases.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2006
 DOI:
 10.1142/S0217751X06031764
 arXiv:
 arXiv:hepth/0508002
 Bibcode:
 2006IJMPA..21.3111B
 Keywords:

 11.10.Nx;
 11.30.Cp;
 Noncommutative field theory;
 Lorentz and Poincare invariance;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Quantum Physics
 EPrint:
 18 pages, LaTex. References added and typos corrected