In this paper we discuss a new type of four-dimensional representation of the braid group. The matrices of braid operations are constructed by $q$ deformation of Hamiltonians. One is Dirac's Hamiltonian for a free electron with mass $m$ , the other, which we find, is related to Bogoliubov's Hamiltonian for quasiparticles in $^{3}\text{H}\text{e}\ensuremath{-}\text{B}$ 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 $\ensuremath{\nu}=1/2$.In this paper we discuss a new type of four-dimensional representation of the braid group. The matrices of braid operations are constructed by $q$ deformation of Hamiltonians. One is Dirac's Hamiltonian for a free electron with mass $m$, the other, which we find, is related to Bogoliubov's Hamiltonian for quasiparticles in $^{3}\text{H}\text{e}\ensuremath{-}\text{B}$ 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 $\ensuremath{\nu}=1/2$.

arXiv:0711.3260Physical Review AJun 3, 20083 citations

Braid Group and Quantum Group of Z(N)Model

Ge Mo

Chinese Science BulletinJan 1, 19931 citation

In this paper we discuss a new type of four-dimensional representation of the braid group. The matrices of braid operations are constructed by

q

deformation of Hamiltonians. One is Dirac's Hamiltonian for a free electron with mass

m

, the other, which we find, is related to Bogoliubov's Hamiltonian for quasiparticles in $^{3}\text{H}\text{e}\ensuremath{-}\text{B}$ 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 $\ensuremath{\nu}=1/2$.