## Proceedings of the International Conference on Geometry, Integrability and Quantization

### An $S^1$-Reduction of Non-Formal Star Product

#### Abstract

Starting from the Moyal product on eight-dimensional canonical Euclidean phase space $T^* \mathbb{R}^4$ with an $S^1$-symplectic action, we construct a non-formal star product, i.e., the deformation parameter is a real number, on the cotangent bundle of three-dimensional Euclidean space except the origin $T^* (\mathbb{R}^3\backslash\{\rm 0\})$ which is the reduced symplectic manifold by the $S^1$-action.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436815709

Digital Object Identifier
doi:10.7546/giq-15-2014-162-172

Mathematical Reviews number (MathSciNet)
MR3287756

Zentralblatt MATH identifier
1318.53103

#### Citation

Kanazawa, Tomoyo; Yoshioka, Akira. An $S^1$-Reduction of Non-Formal Star Product. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 162--172, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-162-172. https://projecteuclid.org/euclid.pgiq/1436815709