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Renormalization group invariance of quantum mechanics. (English) Zbl 0989.81523

Summary: We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of an \(n\)th order derivative equation with respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism. Scaled running potentials for the subtracted equations keep the physics invariant for a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory, is shown.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81T17 Renormalization group methods applied to problems in quantum field theory
82B28 Renormalization group methods in equilibrium statistical mechanics
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