Deformation quantization with separation of variables and gauge theories

Yoshiaki Maeda; Akifumi Sako; Toshiya Suzuki; Hiroshi Umetsu

doi:10.1007/978-3-319-18212-4_9

Deformation quantization with separation of variables and gauge theories

Yoshiaki Maeda, Akifumi Sako, Toshiya Suzuki, Hiroshi Umetsu

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

Abstract

We construct a gauge theory on a noncommutative homogeneous Kähler manifold by using the deformation quantization with separation of variables for Kähler manifolds. A model of noncommutative gauge theory that is connected with an ordinary Yang-Mills theory in the commutative limit is given. As an examples, we review a noncommutative ℂP^N and construct a gauge theory on it. We also give details of the proof showing that the noncommutative ℂP^N constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].

Original language	English
Title of host publication	Geometric Methods in Physics - 33rd Workshop, 2014
Editors	Piotr Kielanowski, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov
Publisher	Springer International Publishing
Pages	135-144
Number of pages	10
ISBN (Print)	9783319182117
DOIs	https://doi.org/10.1007/978-3-319-18212-4_9
Publication status	Published - 2015
Event	33rd Workshop on Geometric Methods in Physics, 2014 - Bialowieza, Poland Duration: 29 Jun 2014 → 5 Jul 2014

Publication series

Name	Trends in Mathematics
Volume	71
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Conference

Conference	33rd Workshop on Geometric Methods in Physics, 2014
Country/Territory	Poland
City	Bialowieza
Period	29/06/14 → 5/07/14

Keywords

Gauge theory
Noncommutative geometry

Access to Document

10.1007/978-3-319-18212-4_9

Cite this

Maeda, Y., Sako, A., Suzuki, T., & Umetsu, H. (2015). Deformation quantization with separation of variables and gauge theories. In P. Kielanowski, P. Bieliavsky, A. Odzijewicz, M. Schlichenmaier, & T. Voronov (Eds.), Geometric Methods in Physics - 33rd Workshop, 2014 (pp. 135-144). (Trends in Mathematics; Vol. 71). Springer International Publishing. https://doi.org/10.1007/978-3-319-18212-4_9

Maeda, Yoshiaki ; Sako, Akifumi ; Suzuki, Toshiya et al. / Deformation quantization with separation of variables and gauge theories. Geometric Methods in Physics - 33rd Workshop, 2014. editor / Piotr Kielanowski ; Pierre Bieliavsky ; Anatol Odzijewicz ; Martin Schlichenmaier ; Theodore Voronov. Springer International Publishing, 2015. pp. 135-144 (Trends in Mathematics).

@inproceedings{4c080c6948dc445c96c942b017f73227,

title = "Deformation quantization with separation of variables and gauge theories",

abstract = "We construct a gauge theory on a noncommutative homogeneous K{\"a}hler manifold by using the deformation quantization with separation of variables for K{\"a}hler manifolds. A model of noncommutative gauge theory that is connected with an ordinary Yang-Mills theory in the commutative limit is given. As an examples, we review a noncommutative ℂPN and construct a gauge theory on it. We also give details of the proof showing that the noncommutative ℂPN constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].",

keywords = "Gauge theory, Noncommutative geometry",

author = "Yoshiaki Maeda and Akifumi Sako and Toshiya Suzuki and Hiroshi Umetsu",

note = "Publisher Copyright: {\textcopyright} 2015 Springer International Publishing Switzerland.; 33rd Workshop on Geometric Methods in Physics, 2014 ; Conference date: 29-06-2014 Through 05-07-2014",

year = "2015",

doi = "10.1007/978-3-319-18212-4\_9",

language = "English",

isbn = "9783319182117",

series = "Trends in Mathematics",

publisher = "Springer International Publishing",

pages = "135--144",

editor = "Piotr Kielanowski and Pierre Bieliavsky and Anatol Odzijewicz and Martin Schlichenmaier and Theodore Voronov",

booktitle = "Geometric Methods in Physics - 33rd Workshop, 2014",

}

Maeda, Y, Sako, A, Suzuki, T & Umetsu, H 2015, Deformation quantization with separation of variables and gauge theories. in P Kielanowski, P Bieliavsky, A Odzijewicz, M Schlichenmaier & T Voronov (eds), Geometric Methods in Physics - 33rd Workshop, 2014. Trends in Mathematics, vol. 71, Springer International Publishing, pp. 135-144, 33rd Workshop on Geometric Methods in Physics, 2014, Bialowieza, Poland, 29/06/14. https://doi.org/10.1007/978-3-319-18212-4_9

Deformation quantization with separation of variables and gauge theories. / Maeda, Yoshiaki; Sako, Akifumi; Suzuki, Toshiya et al.
Geometric Methods in Physics - 33rd Workshop, 2014. ed. / Piotr Kielanowski; Pierre Bieliavsky; Anatol Odzijewicz; Martin Schlichenmaier; Theodore Voronov. Springer International Publishing, 2015. p. 135-144 (Trends in Mathematics; Vol. 71).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Deformation quantization with separation of variables and gauge theories

AU - Maeda, Yoshiaki

AU - Sako, Akifumi

AU - Suzuki, Toshiya

AU - Umetsu, Hiroshi

PY - 2015

Y1 - 2015

N2 - We construct a gauge theory on a noncommutative homogeneous Kähler manifold by using the deformation quantization with separation of variables for Kähler manifolds. A model of noncommutative gauge theory that is connected with an ordinary Yang-Mills theory in the commutative limit is given. As an examples, we review a noncommutative ℂPN and construct a gauge theory on it. We also give details of the proof showing that the noncommutative ℂPN constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].

AB - We construct a gauge theory on a noncommutative homogeneous Kähler manifold by using the deformation quantization with separation of variables for Kähler manifolds. A model of noncommutative gauge theory that is connected with an ordinary Yang-Mills theory in the commutative limit is given. As an examples, we review a noncommutative ℂPN and construct a gauge theory on it. We also give details of the proof showing that the noncommutative ℂPN constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].

KW - Gauge theory

KW - Noncommutative geometry

UR - https://www.scopus.com/pages/publications/84959166182

U2 - 10.1007/978-3-319-18212-4_9

DO - 10.1007/978-3-319-18212-4_9

M3 - Conference contribution

AN - SCOPUS:84959166182

SN - 9783319182117

T3 - Trends in Mathematics

SP - 135

EP - 144

BT - Geometric Methods in Physics - 33rd Workshop, 2014

A2 - Kielanowski, Piotr

A2 - Bieliavsky, Pierre

A2 - Odzijewicz, Anatol

A2 - Schlichenmaier, Martin

A2 - Voronov, Theodore

PB - Springer International Publishing

T2 - 33rd Workshop on Geometric Methods in Physics, 2014

Y2 - 29 June 2014 through 5 July 2014

ER -

Deformation quantization with separation of variables and gauge theories

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