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arXiv · 1212.4897

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

Q. H. Liu·Y. Shen·D. M. Xun·X. Wang
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Abstract

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 αx+iβp, where α and β 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.

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Q. H. Liu, Y. Shen, D. M. Xun, X. Wang. 2012-12-20. On relation between geometric momentum and annihilation operators on a two-dimensional sphere. https://doi.org/10.1142/s0219887813200077

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