Article ID Journal Published Year Pages File Type
1855165 Annals of Physics 2011 13 Pages PDF
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=ψψO=ψψ. We analytically compute the scaling dimension of this operator and determine the propagator 〈0|TOO†|0〉〈0|TOO†|0〉. The operator OO represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.

Research highlights► Nonrelativistic scale anomaly leads to operators with complex scaling dimensions. ► We study an operator O=ψψO=ψψ in quantum mechanics with 1/r2 potenial. ► The propagator of the composite operator is analytically computed.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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