Related papers: The Resolvent Algebra: A New Approach to Canonical…
In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of F{\o}lner C*-algebras, a class of C*-algebras admitting a kind…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields.…
Buchholz and Grundling (Comm. Math. Phys., 272, 699--750, 2007) introduced a C$^\ast$-algebra called the resolvent algebra as a canonical quantisation of a symplectic vector space, and demonstrated that this algebra has several desirable…
We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…
We introduce a novel commutative C*-algebra $C_\mathcal{R}(X)$ of functions on a symplectic vector space $(X,\sigma)$ admitting a complex structure, along with a strict deformation quantization that maps a dense subalgebra of…
Let (X,\sigma) be a symplectic space admitting a complex structure and let R(X,\sigma) be the corresponding resolvent algebra, i.e. the C*-algebra generated by the resolvents of selfadjoint operators satisfying canonical commutation…
The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a…
In this article a new formulation of the Weyl C*-algebra, which has been invented by Fleischhack, in terms of C*-dynamical systems is presented. The quantum configuration variables are given by the holonomies along paths in a graph.…
Let Q and P be the position and momentum operators of a particle in one dimension. It is shown that all compact operators can be approximated in norm by linear combinations of the basic resolvents (aQ + bP - i r)^{-1} for real constants…
New criterion of regularity for representation of canonical commutation relations algebra is given on the basis of concept of an analytical vector.
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag-Kastler axioms, with insights gained in the perturbative…
This paper analyzes the action {\delta} of a Lie algebra X by derivations on a C*-algebra A. This action satisfies an "almost inner" property which ensures affiliation of the generators of the derivations {\delta} with A, and is expressed…
Weyl algebra is a simple noncommutative system used in quantum mechanics. Here I introduce the weyl package, written in the R computing language, which furnishes functionality for working with univariate and multivariate Weyl algebras. The…
In this note we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide conditions at the quantum level sufficient to…
We unify the Kumjian-Renault Weyl groupoid construction with the Lawson-Lenz version of Exel's tight groupoid construction. We do this by utilising only a weak algebraic fragment of the C*-algebra structure, namely its *-semigroup reduct.…
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…
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…