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Communications in Mathematical Physics

, Volume 128, Issue 3, pp 565–592 | Cite as

Isoholonomic problems and some applications

  • R. Montgomery
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • R. Montgomery
    • 1
  1. 1.M.S.R.I.BerkeleyUSA

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