Analysis on q-deformed quantum spaces

Abstract

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and selfcontained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, q-deformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces.

Latex, 94 pages, 4 figures

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Cited by in corpus (9)

• Quantum Dynamics on the three-dimensional q-deformed Euclidean Space
• q-Deformed Superalgebras
• Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework
• Quantum kinematics on q-deformed quantum spaces II, Wave functions on position and momentum space
• Momentum and Position Representations for the q-deformed Euclidean Quantum Space
• Conservation laws for a $q$-deformed nonrelativistic particle
• Non-relativistic Schroedinger theory on q-deformed quantum spaces II, The free non-relativistic particle and its interactions
• Nonrelativistic one-particle problem on $q$-deformed Euclidean space
• Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory