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arXiv · 0711.3260

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

Bao-Xing Xie·Kang Xue·Mo-Lin Ge
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Abstract

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 $ν= 1/2$.

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Bao-Xing Xie, Kang Xue, Mo-Lin Ge. 2008-04-28. Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation. https://doi.org/10.1103/physreva.77.064101

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