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ANNALS OF PHYSICS, vol.327, no.3, pp.935-951, 2012 (SCI-Expanded)
Employing the Foldy-Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chem numbers are equal to the coefficients of the 2 + 1 and 4 + 1 dimensional Chern-Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1 + 1 dimensional descendant of the 2+1 dimensional Chern-Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4 + 1 dimensional Dirac theory is explicitly derived through the Foldy-Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4 + 1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3 + 1 dimensions is proposed. (C) 2011 Elsevier Inc. All rights reserved.