## 7 Citations

### Resolvent algebra in Fock-Bargmann representation

- Mathematics
- 2022

The resolvent algebra R ( X, σ ) associated to a symplectic space ( X, σ ) was introduced by D. Buchholz and H. Grundling as a convenient model of the canonical commutation relation (CCR) in quantum…

### 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…

### Strict deformation quantization of abelian lattice gauge fields

- Mathematics
- 2022

This paper shows how to construct classical and quantum field C*-algebras modeling a $$U(1)^n$$ U ( 1 ) n -gauge theory in any dimension using a novel approach to lattice gauge theory, while…

### Extensions of bundles of C*-algebras

- MathematicsReviews in Mathematical Physics
- 2021

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the [Formula: see text] limit of the…

### Injective Tensor Products in Strict Deformation Quantization

- MathematicsMathematical Physics, Analysis and Geometry
- 2021

The aim of this paper is twofold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and…

### Strict deformation quantization of abelian lattice gauge fields

- MathematicsLetters in Mathematical Physics
- 2022

This paper shows how to construct classical and quantum field C*-algebras modeling a U(1)n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### The Classical–Quantum Correspondence

- Physics, Philosophy
- 2022

This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical…

## References

SHOWING 1-10 OF 16 REFERENCES

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

- Mathematics
- 2004

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

### Deformation quantization of Heisenberg manifolds

- Mathematics
- 1989

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

- Mathematics
- 1938

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

- Mathematics
- 1997

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

- Mathematics
- 1998

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

- Mathematics
- 2008

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

- Mathematics
- 1993

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…