TL;DR
This paper introduces generalized q-integration formulas for quantum spaces like q-deformed Minkowski and Euclidean spaces, extending Jackson's q-integral to higher dimensions with invariance under symmetries.
Contribution
It provides new formulas for q-integration on quantum spaces, enabling invariant integration over 3 and 4-dimensional quantum geometries.
Findings
Formulas for q-integration on quantum Minkowski and Euclidean spaces.
Extension of Jackson's q-integral to higher dimensions.
Invariant integration under translations and rotations.
Abstract
In this article we present formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e. q-deformed Minkowski space and q-deformed Euclidean space in 3 or 4 dimensions. Furthermore, our formulae can be regarded as a generalization of Jackson's q-integral to 3 and 4 dimensions and provide a new possibility for an integration over the whole space being invariant under translations and rotations.
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