Starting with division algebra based on quaternion, we have constructed the generalization of quantum Hall effect from two dimension to four dimension. We have constructed the required Hamiltonian operator and thus obtained its eigen values and eigen functions for four dimensional quantum Hall effect for dyons. The degeneracy of the four dimensional quantum Hall system has been discussed in terms of two integers (P\,and\,Q ) related together where as the integer Q plays the role of Landau level index and accordingly the lowest Landau level has been obtained for four dimensional quantum Hall effect associated with magnetic monopole(or dyons). It is shown that there exists the integer as well the fractional quantum Hall effect and so, the four dimensional quantum Hall system provides a macroscopic number of degenerate states and at appropriate integer or fractional filling factions this system forms an incompressible quantum liquid. Key Words: Quaternion, dyons, Hamiltonian operator, Landau level etc
Comments: 18 Pages.
[v1] 2016-10-05 21:33:05
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