Local gauge and magnetic translation groups

Details Local gauge and magnetic translation groups Local gauge and magnetic translation groups

1998-03-07

arxiv.org/abs/cond-mat/9803082v1

Acta Phys. Pol. A vol. 92 (1997) 399-402

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Latex 2.09, RevTex,3 pages, amsfonts

Scientific paper

The magnetic translation group was introduced as a set of operators T(R)=\exp[-iR.(p-eA/c)/\hbar]. However,these operators commute with the Hamiltonian for an electron in a periodic potential and a uniform magnetic field if the vector potential A (the gauge) is chosen in a symmetric way. It is showed that a local gauge field A_R(r) on a crystal lattice leads to operators, which commute with the Hamiltonian for any (global) gauge field A=A(r). Such choice of the local gauge determines afactor system \omega(R,R')= T(R)T(R') T(R+R')^{-1}, which depends on a global gauge only. Moreover, for any potential A a commutator T(R)T(R')T(R)^{-1}T(R')^{-1} depends only on the magnetic field and not on the gauge.

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