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Gauge Theory of Small Vibrations in Polyatomic Molecules

In: Geometry, Mechanics, and Dynamics

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  • Robert G. Littlejohn
  • Kevin A. Mitchell

Abstract

The problem of small vibrations in polyatomic molecules is examined from the standpoint of gauge theory and fiber bundle theory. The Eckart conventions and their privileged status are given a geometrical interpretation (the Eckart coordinates are shown to be Riemann normal co-ordinates and the Eckart frame is a non-Abelian version of Poincarù gauge). The Hamiltonian is developed in covariant Taylor series and averaged over rapid vibrations to second order. The averaged Hamiltonian is expressed in terms of geometrical objects such as the Riemann and Coriolis curvature tensors on shape space.

Suggested Citation

  • Robert G. Littlejohn & Kevin A. Mitchell, 2002. "Gauge Theory of Small Vibrations in Polyatomic Molecules," Springer Books, in: Paul Newton & Philip Holmes & Alan Weinstein (ed.), Geometry, Mechanics, and Dynamics, chapter 13, pages 407-428, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-21791-8_13
    DOI: 10.1007/0-387-21791-6_13
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