通过限制势和能量截止的新模糊球
New fuzzy spheres through confining potentials and energy cutoffs
摘要：
本文简要地报道了我们最近在全正交群O（D），D=d+1下构造的维数为d= 1，2协变的新模糊球.它们是通过在D维量子粒子上施加适当的能量截止来建立的，该量子粒子受到半径r=1的球体上具有非常尖锐的最小值的限制势阱V（r）的约束;此外，截止和阱的深度取决于自然数L（并与自然数L发散）。坐标的换位子只取决于角动量，就像在斯奈德非对易空间中一样。当L发散时，希尔伯特空间维数也发散; S^d_L收敛于S^d，我们在S^d上恢复了普通的量子力学。这些模型在量子场论、量子引力或凝聚态物理中可能是有用的。
英文摘要：
We briefly report our recent construction of new fuzzy spheres of dimensions d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a suitable energy cutoff on a quantum particle in D dimensions subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r=1; furthermore, the cutoff and the depth of the well depend on (and diverge with) a natural number L. The commutator of the coordinates depends only on the angular momentum, as in Snyder noncommutative spaces. When L diverges, the Hilbert space dimension diverges, too; S^d_L converges to S^d, and we recover ordinary quantum mechanics on S^d. These models might be useful in quantum field theory, quantum gravity or condensed matter physics.
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