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}
}
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83 Citations
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83 Citations

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

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

  • 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…

Quantum Systems and Resolvent Algebras

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

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

  • 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…

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

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

  • 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…

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

  • 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…

C*-Completions and the DFR-Algebra

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

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…
...

References

SHOWING 1-10 OF 34 REFERENCES

Algebraic Supersymmetry: A Case Study

The treatment of supersymmetry is known to cause difficulties in the C*–algebraic framework of relativistic quantum field theory; several no–go theorems indicate that super–derivations and super–KMS…

A host algebra for an infinite dimensional symplectic space

The concept of a host algebra generalizes that of a group C*-algebra to groups which are not locally compact in the sense that nondegenerate representations of the host algebra are in one-to-one…

The C*-algebras of a free Boson field

AbstractWe give a systematic description of severalC*-algebras associated with a free Boson field. In this first part the structure of the one-particle space enters only through its symplectic form σ…

Algebraic quantization of systems with a gauge degeneracy

Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical…

C*-ALGEBRAS GENERATED BY UNBOUNDED ELEMENTS

The main aim of this paper is to provide a proper mathematical framework for the theory of topological non-compact quantum groups, where we have to deal with non-unital C*-algebras. The basic…

On the time evolution automorphisms of the CCR-algebra for quantum mechanics

AbstractIn ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form $$H = \frac{{P^2 }}{{2m}} + V(Q)$$ is studied from the point of view of…

Abelian topological groups with host algebras

The concept of a host algebra generalises that of a group C -algebra to groups which are not locally compact in the sense that nondegenerate representations of the host algebra are in one-to-one…

Local Quantum Constraints

We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of space-time regions. In particular we find "weak" Haag–Kastler axioms which will ensure that…

The dual spaces of *-algebras

Introduction. The idea of the structure space (or dual space) A of an associative algebra A was introduced by Jacobson in [8]. The space A consists of all kernels of irreducible representations of A,…

A note on regular states and supplementary conditions

We show that linear Hermitian supplementary conditions can never be imposed in a representation associated with a regular state on the C*-algebra of the CCRs. Nevertheless, there is a well-defined…