Zeitschrift für Physik C Particles and Fields

, Volume 36, Issue 4, pp 699–714 | Cite as

Path integrals on curved manifolds

  • C. Grosche
  • F. Steiner
Article
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Abstract

A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correctionΔV∼h2 from the classical Lagrangian ℒ, i.e. the correct effective Lagrangian to be used in the path integral is ℒeff = ℒ−ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: Thed-dimensional rotator, i.e. the motion on the sphereSd−1, the path integral ind-dimensional polar coordinates, the exact treatment of the hydrogen atom inR2 andR3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential.

Keywords

Manifold Field Theory Hydrogen Atom Elementary Particle Quantum Field Theory 
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 1987

Authors and Affiliations

  • C. Grosche
    • 1
  • F. Steiner
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Federal Republic of Germany

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