$O^\star$-algebras and quantum dynamics: some existence results

TL;DR

This paper explores defining algebraic quantum dynamics within $O^ riangleright$-algebras without requiring a full Hamiltonian, using limiting procedures from regularized sequences to establish existence under certain conditions.

Contribution

It extends previous work by removing the assumption of a full Hamiltonian, demonstrating the existence of dynamics via limiting procedures in $O^ riangleright$-algebras.

Findings

Dynamics can be defined without a full Hamiltonian.

Limiting procedures from regularized sequences are effective.

Existence results depend on specific conditions.

Abstract

We discuss the possibility of defining an algebraic dynamics within the settings of $O^\star$-algebras. Compared with our previous results on this subject, the main improvement here is that we are not assuming the existence of some hamiltonian for the {\em full} physical system. We will show that, under suitable conditions, the dynamics can still be defined via some limiting procedure starting from a given {\em regularized sequence}.