TL;DR
This paper develops a general framework using variational principles and Faddeev methods to analyze particle propagation on a torus, with applications in quantum chromodynamics and condensed matter physics.
Contribution
It introduces two multiparticle secular equation versions connecting torus and infinite volume dynamics, aiding lattice QCD data analysis and condensed matter studies.
Findings
Two multiparticle secular equations are formulated.
The first version links torus and infinite volume dynamics.
The second version improves robustness for lattice QCD analysis.
Abstract
In this study, based on the variational principle and Faddeev method, we present a general framework for finding the propagating solutions of multiple interacting particles on a torus. Two different versions of multiparticle secular equations are presented. Version one shows how the propagating solutions on a torus and the infinite volume dynamics are connected. The second version may be more suitable and robust for the task of lattice quantum chromodynamics data analysis. The proposed formalism may also be useful for studying the effects of few-body interactions on the electronic band structure in condensed matter physics.
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