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Preface | ||
Ch. 1 | Basics for Quantum Groups | |
1 | Preliminary Ideas | |
2 | Braiding | |
Ch. 2 | Calculus and Algebra | |
1 | Integration and Fourier Transform | |
Ch. 3 | Differential Calculi | |
1 | Differential Calculi I | |
2 | Differential Calculi II | |
3 | Differential Calculi III | |
4 | Further Remarks on Differential Calculi | |
Ch. 4 | More on Q-Analysis | |
1 | Quantum Planes | |
2 | Remarks on Quantum Planes | |
3 | Further Details on Q-Analysis | |
4 | The Heisenberg Algebra | |
Ch. 5 | Remarks on Quantum Transmutation | |
1 | Introduction | |
2 | Some Quantum Transmutations | |
3 | Classical Transmutation | |
4 | Some Q-Calculus | |
5 | Fourier Transforms and Distributions | |
6 | Some Preliminary Calculations | |
7 | Quantum Intertwining | |
Ch. 6 | Discretization and Quantum Mechanics | |
1 | Preliminary Remarks | |
2 | Discretization and Moyal | |
3 | Q-Discretization | |
4 | Calculations | |
5 | Connections to Integrability | |
6 | KP and DKP | |
7 | Remarks on Q-KP | |
8 | Remarks on Star Products | |
Ch. 7 | Discrete Calculus | |
1 | Differential Calculus on Finite Sets | |
2 | Finite Quantum Physics | |
Ch. 8 | Fuzzy Physics and Matrix Geometry | |
1 | The Fuzzy Sphere | |
2 | Aspects of Noncommutative Geometry | |
3 | WZW | |
4 | Coherent States | |
Ch. 9 | Further Aspects of FQM | |
1 | Spectral Triples and Distance | |
2 | Discrete Riemannian Geometry | |
3 | Remarks on Lattice Gauge Theory | |
4 | Connections to Gravity | |
5 | Knots and the KZ Equation | |
Ch. 10 | Integrable Systems | |
1 | Generalized Sigma Models | |
2 | Bicomplexes | |
Ch. 11 | Aspects of Gauge Theory | |
1 | Some Background | |
2 | Gauge Theory on NC Spaces | |
3 | Summary and Recapitulation | |
Ch. 12 | Pointless Spaces and Quantum Gravity | |
1 | Introduction | |
2 | Pointless Spaces | |
3 | Singularities | |
Bibliography | ||
Index |
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