Quantization and the resolvent algebra

@article{vanNuland2019QuantizationAT,
  title={Quantization and the resolvent algebra},
  author={Teun D. H. van Nuland},
  journal={Journal of Functional Analysis},
  year={2019}
}

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References

SHOWING 1-10 OF 16 REFERENCES

Field-theoretic Weyl Quantization as a Strict and Continuous Deformation Quantization

Abstract. For an arbitrary (possibly infinite-dimensional) pre-symplectic test function space $$ (E, \sigma) $$ the family of Weyl algebras $$ \{\mathcal{W}(E,

Deformation quantization for actions of Qpd

The Resolvent Algebra: A New Approach to Canonical Quantum Systems

Deformation quantization of Heisenberg manifolds

ForM a smooth manifold equipped with a Poisson bracket, we formulate aC*-algebra framework for deformation quantization, including the possibility of invariance under a Lie group of diffeomorphisms

On integration in vector spaces

Introduction. Several authors ([3]-[10], inclusive; [15])t have already given generalized Lebesgue integrals for functions x(s) whose values lie in a Banach space (B-space) X.: In the following pages

Deformation Quantization for Hilbert Space Actions

Abstract:Rieffel's theory of deformations of C*-algebras for -actions can be extended to actions of infinite-dimensional Hilbert spaces. The CCR algebra over a Hilbert space H can be exhibited in

Mathematical Topics Between Classical and Quantum Mechanics

Introductory Overview.- I. Observables and Pure States.- Observables.- Pure States.- From Pure States to Observables.- II. Quantization and the Classical Limit.- Foundations.- Quantization on Flat

An Obstruction to Quantization of the Sphere

In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter ħ is not connected; indeed, it is almost discrete. Li

Deformation Quantization for Actions of R ]D

Oscillatory integrals The deformed product Function algebras The algebra of bounded operators Functoriality for the operator norm Norms of deformed deformations Smooth vectors, and exactness