Abstract
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.
Highlights
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques
A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization
D dimensions using cutoff regularization in configuration space; (ii) present a complete picture of the renormalized theory; and (iii) confirm the same conclusions using dimensional regularization [9]. This problem is crucial for the analysis and interpretation of the point dipole interaction of molecular physics [10,11], and may be relevant in polymer physics
Summary
Horacio E., "Renormalization of the Inverse Square Potential" (2001). The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization.
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