# Strict deformation quantization of a particle in external gravitational and Yang-Mills fields

@article{Landsman1993StrictDQ, title={Strict deformation quantization of a particle in external gravitational and Yang-Mills fields}, author={Nicolaas P. Landsman}, journal={Journal of Geometry and Physics}, year={1993}, volume={12}, pages={93-132} }

## 69 Citations

### Geometric Quantization of the Phase Space of a Particle in a Yang-Mills Field

- Physics, Mathematics
- 1994

### Cotangent bundle quantization : entangling of metric and magnetic field

- Mathematics
- 2005

For manifolds of noncompact type endowed with an affine connection (for example, the Levi–Civita connection) and a closed 2-form (magnetic field), we define a Hilbert algebra structure in the space…

### Twisted Lie Group C*-Algebras as Strict Quantization

- Mathematics
- 1998

A nonzero 2-cocycle Γ∈ Z2(g, R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie–Poisson structure on the dual Lie algebra g*, leading to a Poisson algebra C∞…

### Lie Groupoid C*-Algebras and Weyl Quantization

- Mathematics
- 1999

Abstract:A strict quantization of a Poisson manifold P on a subset containing 0 as an accumulation point is defined as a continuous field of , with , a dense subalgebra on which the Poisson bracket…

### 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…

### Quantization of Poisson algebras associated to Lie algebroids

- Mathematics
- 2000

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded…

### Deformation quantization on the cotangent bundle of a Lie group

- MathematicsJournal of Mathematical Physics
- 2018

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced…

### Classical and quantum representation theory

- Mathematics
- 1994

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In…

### QUANTIZATION OF SYMPLECTIC REDUCTION

- Mathematics
- 1999

Symplectic reduction, also known as Marsden-Weinstein reduction, is an important construction in Poisson geometry. Following N.P. Landsman [22], we propose a quantization of this procedure by means…

## References

SHOWING 1-10 OF 52 REFERENCES

### Deformations of Algebras of Observables and the Classical Limit of Quantum Mechanics

- Mathematics, Physics
- 1993

The quantum algebra of observables of a particle moving on a homogeneous configuration space Q = G/H, the transformation group C*-algebra C* (G, G/H), is deformed into its classical counterpart C0…

### INDUCED REPRESENTATIONS, GAUGE FIELDS, AND QUANTIZATION ON HOMOGENEOUS SPACES

- Mathematics
- 1992

We study representations of the enveloping algebra of a Lie group G which are induced by a representation of a Lie subgroup H, assuming that G/H is reductive. Such representations describe the…

### Poisson cohomology and quantization.

- Mathematics
- 1990

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending…

### QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS

- Mathematics
- 1990

Quantization is defined as the act of assigning an appropriate C*-algebra to a given configuration space Q, along with a prescription mapping self-adjoint elements of into physically interpretable…

### Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures

- Mathematics
- 1990

Introduction. Let L be a finite dimensional Lie algebra over the real numbers, R, and let L* be its dual vector space. It is well-known [24] that the Lie algebra structure on L defines a natural…

### Classical and quantum representation theory

- Mathematics
- 1994

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In…

### 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…

### Coisotropic calculus and Poisson groupoids

- Mathematics
- 1988

Lagrangian submanif olds play a special role in the geometry of symplectic manifolds. From the point of view of quantization theory, or simply a categorical approach to symplectic geometry [Gu-S2],…

### Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations

- Mathematics
- 1984

Wong [14] introduced equations of motion for a spin 0 particle in a Yang-Mills field which was widely accepted among physicists. It is shown that these are equivalent to the various mathematical…