Communications in Mathematical Physics

, Volume 129, Issue 3, pp 481–509 | Cite as

Integration on thenth power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations)

  • Bent Fuglede


The integral of a function over then'th power of hyperbolicd-dimensional spaceH is decomposed into integration along each orbit under diagonal action onHn of the isometry groupG onH, followed by integration over the orbit space, parametrized in terms of a complete set of invariants. The Jacobian entering in this last integral is expressed explicitly in terms of certain determinants. When viewingH as a half-hyperboloid in ℝ d+1 ,G is induced by the homogeneous Lorentz groupO(1,d) acting on ℝ d+1 .


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Bent Fuglede
    • 1
  1. 1.Matematisk InstitutKøbenhavns UniversitetKøbenhavn øDenmark

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