The resolvent algebra of non-relativistic Bose fields: observables, dynamics and states

TL;DR

This paper analyzes the structure of the gauge invariant C*-algebra for non-relativistic Bose fields, showing its stability under dynamics and implications for describing interacting bosons and simplifying state construction.

Contribution

It demonstrates that the gauge invariant algebra forms a dense subalgebra of an inverse limit of AF-algebras and remains stable under Hamiltonian dynamics, enabling new approaches in many-body theory.

Findings

The algebra is a dense subalgebra of an inverse limit of AF-algebras.

The algebra is stable under Hamiltonian dynamics with pair potentials.

This approach simplifies the construction of infinite bosonic states.

Abstract

The structure of the gauge invariant (particle number preserving) C*-algebra generated by the resolvents of a non-relativistic Bose field is analyzed. It is shown to form a dense subalgebra of the bounded inverse limit of a system of approximately finite dimensional C*-algebras. Based on this observation, it is proven that the closure of the gauge invariant algebra is stable under the dynamics induced by Hamiltonians involving pair potentials. These facts allow to proceed to a description of interacting Bosons in terms of C*-dynamical systems. It is outlined how the present approach leads to simplifications in the construction of infinite bosonic states and sheds new light on topics in many body theory.