ISOHOLONOMIC PROBLEMS AND SOME APPLICATIONS

被引：109

作者：

MONTGOMERY, R

机构：

[1] M.S.R.I., Berkeley, 94720, CA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1990年 / 128卷 / 03期

关键词：

D O I：

10.1007/BF02096874

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the problem of finding the shortest loops with a given holonomy. We show that the solutions are the trajectories of particles in Yang-Mills potentials (Theorem 4), or, equivalently, the projections of Kaluza-Klein geodesics (Theorem 2). Applications to quantum mechanics (Berry's phase, Sect. 3) and the optimal control of deformable bodies (Sect. 6) are touched upon. © 1990 Springer-Verlag.

引用

页码：565 / 592

页数：28

共 43 条

[1] PHASE-CHANGE DURING A CYCLIC QUANTUM EVOLUTION [J].

AHARONOV, Y ;

ANANDAN, J .

PHYSICAL REVIEW LETTERS, 1987, 58 (16) :1593-1596

[2]

Arnol'd VI, 1961, SOV MATH DOKL, V2, P562

[3]

ARNOLD VI, 1988, ENCY MATH SCI SERIES, V3

[4] CHERN NUMBERS, QUATERNIONS, AND BERRY PHASES IN FERMI SYSTEMS [J].

AVRON, JE ;

SADUN, L ;

SEGERT, J ;

SIMON, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 124 (04) :595-627

[5]

Baillieuls J., 1975, J OPTIMIZATION TH AP, V25, P519

[6] LAGRANGIAN AND HAMILTONIAN DESCRIPTIONS OF YANG-MILLS PARTICLES [J].

BALACHANDRAN, AP ;

BORCHARDT, S ;

STERN, A .

PHYSICAL REVIEW D, 1978, 17 (12) :3247-3256

[7]

BAR C, 1989, GEODESICS CARNOT CAR

[8]

BAR C, 1988, THESIS BONN

[9] CLASSICAL ADIABATIC ANGLES AND QUANTAL ADIABATIC PHASE [J].

BERRY, MV .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1985, 18 (01) :15-27

[10]

BLISS GA, 1930, AM J MATH, V52, P674

← 1 2 3 4 5 →