TL;DR
This paper introduces a general algebraic method for constructing operators in n-body systems, extending two-body relations to any number of particles using tensor algebra and coalgebra structures, with applications to various symmetry algebras.
Contribution
It presents a novel, systematic approach to build global and relative operators for n-body systems based on properties of algebra morphisms and coalgebra structures.
Findings
Method applicable to Galilei, Poincare, and deformed Galilei algebras
Enables generalization of two-body relations to n-body systems
Provides explicit constructions for algebraic operators in multi-particle systems
Abstract
A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the kinematics and it allows also the generalization to any n of relations demon- strated for two. The coalgebra structures play a peculiar role in the explicit constructions. Three examples are presented concerning the Galilei, Poincare' and deformed Galilei algebras.
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