Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-15
Physics
High Energy Physics
High Energy Physics - Theory
5 pages, minor improvements and references added
Scientific paper
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is completely independent of both the geometry and topology of the Riemann surface. The formula is obtained by reinterpreting the quantum Hamiltonian as the second variation operator of an associated classical variational problem.
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