کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1855090 | 1529930 | 2009 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Discrete accidental symmetry for a particle in a constant magnetic field on a torus Discrete accidental symmetry for a particle in a constant magnetic field on a torus](/preview/png/1855090.png)
A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r1/r and r2r2 potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge–Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θθ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θxθx and θyθy explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.
Journal: Annals of Physics - Volume 324, Issue 2, February 2009, Pages 343–360