Friday, December 21, 2012

1212.4897 (Q. H. Liu et al.)

On relation between geometric momentum and annihilation operators on a
two-dimensional sphere
   [PDF]

Q. H. Liu, Y. Shen, D. M. Xun, X. Wang
With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihilation operators whose eigenstates are coherent states on the sphere take the expected form {\alpha}x+i{\beta}p, where {\alpha} and {\beta} are two operators that depend on the angular momentum and x and p are the position and the geometric momentum, respectively. Since the geometric momentum is manifestly a consequence of embedding the two-dimensional sphere in the three-dimensional flat space, the coherent states reflects some aspects beyond the intrinsic geometry of the surfaces.
View original: http://arxiv.org/abs/1212.4897

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