Covariant and dynamical reduction for principal bundle field theories

被引：7

作者：

Castrillon Lopez, Marco ^{[1
]}

Marsden, Jerrold E. ^{[2
]}

机构：

[1] Univ Complutense Madrid, Dept Geometria & Topol, E-28040 Madrid, Spain

[2] CALTECH, Pasadena, CA 91125 USA

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2008年 / 34卷 / 03期

基金：

美国国家科学基金会;

关键词：

variational calculus; symmetries; reduction; Euler-Poincare equations;

D O I：

10.1007/s10455-008-9108-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Reduction for field theories with symmetry can be done either covariantly-that is, on spacetime-or dynamically-that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a "sea of rigid bodies" with and appropriate interbody coupling potential.

引用

页码：263 / 285

页数：23

共 14 条

[11] Reduction in principal bundles:: Covariant Lagrange-Poincare equations [J].

López, MC ;

Ratiu, TS .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 236 (02) :223-250

[12]

López MC, 2001, LETT MATH PHYS, V58, P167

[13] The geometry of the bundle of connections [J].

López, MC ;

Masqué, JM .

MATHEMATISCHE ZEITSCHRIFT, 2001, 236 (04) :797-811

[14]

Marsden J. E., 1999, Introduction to Mechanics and Symmetry-A Basic Exposition of Classical Mechanical Systems, V2nd ed., DOI 10.1007/978-0-387-21792-5

← 1 2 →