q-Integration on Quantum Spaces

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.

38 pages, Latex, corrected typos, major modifications to improve clarity

References in corpus (5)

• Gauge Theory on Noncommutative Spaces
• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• The $S{O}_q(N,\mathbf{R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\mathbf{R}}_q^N$ and its Hilbert Space Structure
• Integration on quantum Euclidean space and sphere in $N$ dimensions
• *-Products on Quantum Spaces

Cited by in corpus (19)

• Thermostatistics of deformed bosons and fermions
• q-Deformed quantum Lie algebras
• Deformed quantum statistics in two-dimensions
• q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
• Analysis on q-deformed quantum spaces
• q-Exponentials on quantum spaces
• q-Translations on quantum spaces
• Braided products for quantum spaces
• Superanalysis on quantum spaces
• Grassmann variables on quantum spaces
• Quantum Dynamics on the three-dimensional q-deformed Euclidean Space
• The Fourier Transform on Quantum Euclidean Space
• q-Deformed Superalgebras
• Momentum and Position Representations for the q-deformed Euclidean Quantum Space
• Non-relativistic Schroedinger theory on q-deformed quantum spaces I, Mathematical framework and equations of motion
• Conservation laws for a $q$-deformed nonrelativistic particle
• Nonrelativistic one-particle problem on $q$-deformed Euclidean space
• Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space
• Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework