The Resolvent Algebra: A Novel Approach to Canonical Quantum Systems

The Resolvent Algebra: A Novel Approach to Canonical Quantum Systems

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Detlev Buchholz, University of Göttingen
Jadwin Hall 343

The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the automorphic action of physically interesting dynamics nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. In this talk a novel C*-algebra of the canonical commutation relations is presented which is based on the resolvents of the canonical operators. It has many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, it provides a convenient framework for the study of (infinite) interacting quantum systems and of constraints, as will be illustrated by several examples.