Integration on thenth power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations)
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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 .
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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- 1.Bogoliubov, N. N., Logunov, A. A., Todorov, I. T.: Introduction to axiomatic quantum field theory. Reading. Massachusetts: Benjamin 1975Google Scholar
- 2.Fenchel, W.: Elementary geometry in hyperbolic space. Berlin, New York: De Gruyter 1989Google Scholar
- 3.Hall, D., Wightman, A. S.: A theorem on invariant analytic functions with applications to relativistic quantum field theory. Mat.-Fys. Medd. Dan. Vid. Selsk.31, 41 (1957)Google Scholar