Fixed-Point Few-Body Hamiltonians in Quantum Mechanics

TL;DR

This paper revisits fixed-point Hamiltonians in quantum few-body systems, emphasizing renormalization techniques for singular interactions and extending the formalism from two- to three- and four-body systems.

Contribution

It introduces a revised formulation of subtracted scattering equations and fixed-point Hamiltonians for singular interactions, extending the renormalization framework to three- and four-body systems.

Findings

Effective treatment of singular interactions in two-nucleon systems

Extension of renormalization formalism to three-body systems

Discussion on applications to four-particle systems

Abstract

We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in the limit of short-range interactions. In this context, it is revised the formulation of the subtracted scattering equations and fixed-point Hamiltonians applied to few-body systems, in which the original interaction contains point-like singularities, such as Dirac-delta and/or its derivatives. The approach is being illustrated by considering two-nucleons described by singular interactions. This revision also includes an extension of the renormalization formalism to three-body systems, which is followed by an updated discussion on the applications to four particles.