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arXiv · 1007.4635

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

Sergej Moroz
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Abstract

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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Sergej Moroz. 2010-07-27. Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions. https://doi.org/10.1016/j.aop.2011.01.003

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