Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

Details Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

2007-11-21

arxiv.org/abs/0711.3260v2

Physics

Quantum Physics

3 pages, 5 figures

Scientific paper

10.1103/PhysRevA.77.064101

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu = 1/2$.

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