Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

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=ψψ. 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.

18 pages, 3 figures; published version

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• Path-Integral Derivation of the Non-relativistic Scale Anomaly
• Critical ageing correlators from Schrödinger-invariance
• Schrödinger-invariance in the voter model