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

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 $S{O}_q(N)$. 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.

15 pages, Latex, citations and reference added, minor typos corrected

Cited by in corpus (15)

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• q-Integration on Quantum Spaces
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• The Geometry of the Quantum Euclidean Space
• q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
• Analysis on q-deformed quantum spaces
• Twisted submanifolds of R^n
• q-Quaternions and q-deformed su(2) instantons
• q-Deformed su(2) instantons by q-quaternions
• On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N
• Gauge Field Theory on the E_q(2)-covariant Plane
• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$
• q-Deformed quaternions and su(2) instantons
• Frame formalism for the N-dimensional quantum Euclidean spaces