arXiv subjects

M. Elbistan

Publications and source records attributed to M. Elbistan.

22 records · Page 2Linked to original sources

arXiv2015

Wigner-Souriau translations and Lorentz symmetry of chiral fermions

Chiral fermions can be embedded into Souriau's massless spinning particle model by "enslaving" the spin, viewed as a gauge constraint. The latter is not invariant under Lorentz boosts; spin enslavement can be restored, however, by a subsequent Wigner-Souriau (WS) translation, analogous to a compensating gauge transformation. The combined transformation is precisely the recently uncovered twisted boost, which we now extend to finite transformations. WS-translations are identified with the stability group of a motion acting on the right on the Poincare group, whereas the natural Poincare action corresponds to action on the left. The relation to non-commutative mechanics is explained.

hep-th↗

arXiv2013

3+1 dimensional topological field theory as the effective action of neutral fermions

We proposed an action of neutral fermions interacting with external electromagnetic fields to construct a 3+1 dimensional topological field theory as the effective action attained by integrating out the fermionic fields in the related path integral. These neutral quasiparticles are assumed to emerge from the collective behavior of the original physical particles and holes (antiparticles). Although our construction is general it is particularly useful to formulate effective actions of the time reversal invariant topological insulators.

math-ph↗

arXiv2012

Effective field theory of topological insulator and the Foldy-Wouthuysen transformation

Employing the Foldy-Wouthuysen transformation it is demonstrated straightforwardly that the first and second Chern 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.

math-ph↗

arXiv2009

Spin Hall Effect in Noncommutative Coordinates

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter theta . The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and θdeformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting θdifferent formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.

hep-th↗