Fixed-Point Few-Body Hamiltonians in Quantum Mechanics

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.

27 pages, 2 figures

References in corpus (8)

• Comparing and contrasting nuclei and cold atomic gases
• Four-boson scale near a Feshbach resonance
• $N$-boson spectrum from a Discrete Scale Invariance
• Neutron${-}^{19}$C scattering near an Efimov state
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Neutron${-}^{19}$C scattering: emergence of universal properties in a finite range potential
• Probing the Efimov discrete scaling in atom-molecule collision
• Renormalization of chiral nuclear forces with multiple subtractions in peripheral channels