# 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}
}
• Published 14 May 2007
• Mathematics
• Journal of Functional Analysis
83 Citations
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
• D. Buchholz
• Physics, Mathematics
Communications 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
• 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
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
• D. Buchholz
• Mathematics
Communications 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
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
• D. Buchholz
• Mathematics, Physics
Communications 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
• D. Buchholz
• Mathematics, Physics
Communications 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
• 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
• 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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