Effective field theory program for conformal quantum anomalies

Abstract

The emergence of conformal states is established for any problem involving a domain of scales where the long-range SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs is in place, this renormalization mechanism is capable of producing binding in the strong-coupling regime. A realization of this phenomenon, in the form of dipole-bound anions, is discussed.

Renormalization in conformal quantum mechanics

“…Moreover, such bounds enhance the predictability of the conformal approach by quantifying corrections associated with the existence of an infrared cutoff, as shown in Ref. [18]-where these techniques are applied to the formation of molecular dipole-bound anions.…”

“…9 ln (r B /a) 2 2 (in which δ absorbs ultraviolet and infrared corrections), with remarkable numerical accuracy [18].…”

“…[30] is in sharp contrast with the conformal approach: as shown in Ref. [18], the physical origin of criticality and the physics of the logarithmic corrections to the critical dipole moment are traced directly to the presence of a conformal window of scales and its associated renormalization-with the rotational dynamics merely setting the infrared scale. Thus, using the parameters L UV and L IR , a systematic approximation scheme can be introduced to account for the effects of the rotational degrees of freedom-for example, the critical dipole moment λ ( * ) = λ…”

On the inequivalence of renormalization and self-adjoint extensions for quantum singular interactions

“…Refs. [11,12]. In essence, a properly physical quantum anomaly is realized for strong coupling, where binding occurs [as in Eq.…”

“…Consequently, the standard technology of regular quantum mechanics is supplemented by a mandatory regularization toolbox: either Von Neumann's method of self-adjoint extensions [3,4,5,6], which addresses the boundary-value problem, or field-theory renormalization [7,8,9,10,11,12], which deals with the underlying ultraviolet cause of such indeterminacy.…”