Momentum Sections in Hamiltonian Mechanics and Sigma Models

被引：7

作者：

Ikeda, Noriaki ^{[1
]}

机构：

[1] Ritsumeikan Univ, Dept Math Sci, Kusatsu, Shiga 5258577, Japan

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2019年 / 15卷

关键词：

symplectic geometry; Lie algebroid; Hamiltonian mechanics; nonlinear sigma model; LIE ALGEBROIDS; GEOMETRY;

D O I：

10.3842/SIGMA.2019.076

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic manifold by considering gauged sigma models on higher-dimensional manifolds.

引用

页数：16

共 27 条

[1] ATLAS Collaboration, 2018, JHEP, V3, P95, DOI DOI 10.1007/JHEP08(2016)159
[2] Blohmann C., ARXIV181111109
[3] GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY
Blohmann, Christian
Barbosa Fernandes, Marco Cezar
Weinstein, Alan
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2013, 15 (01)
[4] Hidden isometry of "T-duality without isometry"
Bouwknegt, Peter
Bugden, Mark
Klimcik, Ctirad
Wright, Kyle
[J]. JOURNAL OF HIGH ENERGY PHYSICS, 2017, (08):
[5] Reduction of Courant algebroids and generalized complex structures
Bursztyn, Henrique
Cavalcanti, Gil R.
Gualtieri, Marco
[J]. ADVANCES IN MATHEMATICS, 2007, 211 (02) : 726 - 765
[6] PATH-INTEGRAL DERIVATION OF QUANTUM DUALITY IN NONLINEAR SIGMA-MODELS
BUSCHER, TH
[J]. PHYSICS LETTERS B, 1988, 201 (04) : 466 - 472
[7] A SYMMETRY OF THE STRING BACKGROUND FIELD-EQUATIONS
BUSCHER, TH
[J]. PHYSICS LETTERS B, 1987, 194 (01) : 59 - 62
[8] Homotopy moment maps
Callies, Martin
Fregier, Yael
Rogers, Christopher L.
Zambon, Marco
[J]. ADVANCES IN MATHEMATICS, 2016, 303 : 954 - 1043
[9] Carinena J. F., 1991, Differential Geometry and its Applications, V1, P345, DOI 10.1016/0926-2245(91)90013-Y
[10] Cavalcanti GR, 2010, CRM PROC & LECT NOTE, V50, P341

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