Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

Details Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

2010-07-27

arxiv.org/abs/1007.4635v2

Annals Phys.326:1368-1380,2011

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 3 figures; published version

Scientific paper

10.1016/j.aop.2011.01.003

It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O=\psi\psi. We analytically compute the scaling dimension of this operator and determine the propagator <0|T O O^{\dagger}|0>. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.

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