Local Gauge and Magnetic Translation Groups |
| W. Florek Institute of Physics, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland |
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| The magnetic translation group was introduced as a set of operators T(R)=exp[-iR·(p-eA/c)/h]. 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 AR(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 a factor system ω(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)-1T(R')-1 depends only on the magnetic field and not on the gauge. |
| DOI: 10.12693/APhysPolA.92.399 PACS numbers: 02.20.-a, 71.45.-d, 11.15.Ha, 05.50.+q |