Integration on quantum Euclidean space and sphere in $N$ dimensions

Harold Steinacker

doi:10.1063/1.531658

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arXiv · q-alg/9506020

Integration on quantum Euclidean space and sphere in $N$ dimensions

Harold Steinacker

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Abstract

Invariant integrals of functions and forms over $q$ - deformed Euclidean space and spheres in $N$ dimensions are defined and shown to be positive definite, compatible with the star - structure and to satisfy a cyclic property involving the $D$ - matrix of $SO_q(N)$. The definition is more general than the Gaussian integral known so far. Stokes theorem is proved with and without spherical boundary terms, as well as on the sphere.

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BibTeX RIS

Harold Steinacker. 1995-08-04. Integration on quantum Euclidean space and sphere in $N$ dimensions. https://doi.org/10.1063/1.531658

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