Cluster Transformation Coefficients for Structure and Dynamics Calculations in n-Particle Systems: Atoms, Nuclei, and Quarks

TL;DR

This paper introduces a nonperturbative method using cluster transformation coefficients and dynamic linearization to analyze the structure and dynamics of complex n-particle systems, including atoms, nuclei, and quarks.

Contribution

It develops a novel approach combining cluster transformation coefficients with dynamic linearization to solve nonlinear commutator equations in many-particle systems.

Findings

Efficient calculation of matrix elements using group properties.

Application to fermionic and bosonic systems demonstrated.

Identification of superconductive diagrams in 3-quark systems.

Abstract

The structure and dynamics of an n-particle system are described with coupled nonlinear Heisenberg's commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via particle-particle and particle-hole excitations. Nonperturbative solutions of the system are obtained with the use of dynamic linearization approximation and cluster transformation coefficients. The dynamic linearization approximation converts the commutator chain into an eigenvalue problem. The cluster coefficients factorize the matrix elements of the (n)-particles or particle-hole systems in terms of the matrix elements of the (n-1)-systems coupled to a particle-particle, particle-hole, and hole-hole boson. Group properties of the particle-particle, particle-hole, and hole-hole permutation groups simplify the calculation of these coefficients. The particle-particle vacuum-excitations generate superconductive diagrams in the dynamics of 3-quarks systems. Applications of the model to fermionic and bosonic systems are discussed.