Hall effect and lowest Landau level quantum field

Author: merab eliashvili
Co-authors: George Tsitsishvili
Keywords: QHE, LLL, Lagrangiian, desity operator
Annotation:

In the case of the strong magnetic field quantum field theory description of QHE requires projection on the LLL (lowest Landau level). As an alternative to the such projection we consider non relativistic matter quantum field corresponding to the LLL states. We construct action functional and density operator. This scheme may be generalized to the relativistic (Dirac ) field in 2+1 dimensions . This generalization may be relevant for the description of QHE observed in the Graphene.