dorsal/arxiv
View SchemaHomogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation
| Authors | Martin Bordemann, Nikolai Neumaier, Stefan Waldmann |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707030 |
| URL | https://arxiv.org/abs/q-alg/9707030 |
| DOI | 10.1007/s002200050481 |
Abstract
In this paper we construct homogeneous star products of Weyl type on every cotangent bundle $T^*Q$ by means of the Fedosov procedure using a symplectic torsion-free connection on $T^*Q$ homogeneous of degree zero with respect to the Liouville vector field. By a fibrewise equivalence transformation we construct a homogeneous Fedosov star product of standard ordered type equivalent to the homogeneous Fedosov star product of Weyl type. Representations for both star product algebras by differential operators on functions on $Q$ are constructed leading in the case of the standard ordered product to the usual standard ordering prescription for smooth complex-valued functions on $T^*Q$ polynomial in the momenta (where an arbitrary fixed torsion-free connection $\nabla_0$ on $Q$ is used). Motivated by the flat case $T^* R^n$ another homogeneous star product of Weyl type corresponding to the Weyl ordering prescription is constructed. The example of the cotangent bundle of an arbitrary Lie group is explicitly computed and the star product given by Gutt is rederived in our approach.
{
"annotation_id": "38cd7bfb-f7f4-450e-b383-8307a151ffc2",
"date_created": "2026-03-02T18:01:28.527000Z",
"date_modified": "2026-03-02T18:01:28.527000Z",
"file_hash": "b85f2898609afcafc4c2398e73487f2fd5fbd81c37e82304826e04dae4f224eb",
"private": false,
"record": {
"abstract": "In this paper we construct homogeneous star products of Weyl type on every\ncotangent bundle $T^*Q$ by means of the Fedosov procedure using a symplectic\ntorsion-free connection on $T^*Q$ homogeneous of degree zero with respect to\nthe Liouville vector field. By a fibrewise equivalence transformation we\nconstruct a homogeneous Fedosov star product of standard ordered type\nequivalent to the homogeneous Fedosov star product of Weyl type.\nRepresentations for both star product algebras by differential operators on\nfunctions on $Q$ are constructed leading in the case of the standard ordered\nproduct to the usual standard ordering prescription for smooth complex-valued\nfunctions on $T^*Q$ polynomial in the momenta (where an arbitrary fixed\ntorsion-free connection $\\nabla_0$ on $Q$ is used). Motivated by the flat case\n$T^* R^n$ another homogeneous star product of Weyl type corresponding to the\nWeyl ordering prescription is constructed. The example of the cotangent bundle\nof an arbitrary Lie group is explicitly computed and the star product given by\nGutt is rederived in our approach.",
"arxiv_id": "q-alg/9707030",
"authors": [
"Martin Bordemann",
"Nikolai Neumaier",
"Stefan Waldmann"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/s002200050481",
"title": "Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation",
"url": "https://arxiv.org/abs/q-alg/9707030"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9480abf7-06e2-483a-8159-f427f153d429",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}