# The Resolvent Algebra: A New Approach to Canonical Quantum Systems

@article{Buchholz2007TheRA, title={The Resolvent Algebra: A New Approach to Canonical Quantum Systems}, author={Detlev Buchholz and Hendrik B. Grundling}, journal={Journal of Functional Analysis}, year={2007}, volume={254}, pages={2725-2779} }

## 83 Citations

### The Resolvent Algebra of Non-relativistic Bose Fields: Observables, Dynamics and States

- Physics, Mathematics
- 2017

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…

### The Resolvent Algebra of Non-relativistic Bose Fields: Observables, Dynamics and States

- Physics, MathematicsCommunications in Mathematical Physics
- 2018

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…

### Quantum Systems and Resolvent Algebras

- Mathematics
- 2013

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…

### On quasi-free dynamics on the resolvent algebra

- Mathematics
- 2014

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…

### The Resolvent Algebra for Oscillating Lattice Systems: Dynamics, Ground and Equilibrium States

- MathematicsCommunications in Mathematical Physics
- 2017

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…

### The Resolvent Algebra for Oscillating Lattice Systems: Dynamics, Ground and Equilibrium States

- Mathematics
- 2016

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…

### The Resolvent Algebra of Non-relativistic Bose Fields: Sectors, Morphisms, Fields and Dynamics

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2020

It was recently shown that the resolvent algebra of a non-relativistic Bose field determines a gauge invariant (particle number preserving) kinematical algebra of observables which is stable under…

### The Resolvent Algebra of Non-relativistic Bose Fields: Sectors, Morphisms, Fields and Dynamics

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2020

It was recently shown that the resolvent algebra of a non-relativistic Bose field determines a gauge invariant (particle number preserving) kinematical algebra of observables which is stable under…

### C*-Completions and the DFR-Algebra

- Mathematics
- 2014

The aim of this paper is to present the construction of a general family of C*-algebras which includes, as a special case, the "quantum spacetime algebra" introduced by Doplicher, Fredenhagen and…

### Classical and quantised resolvent algebras for the cylinder

- Mathematics
- 2020

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…

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