| Preface | vii |
| Prologue: Some Matters of Notation | 3 |
| Chapter 1. | The Heisenberg Group and Its Representations | 9 |
| 1. | Background from physics | 9 |
| Hamiltonian mechanics | 10 |
| Quantum mechanics | 12 |
| Quantization | 15 |
| 2. | The Heisenberg group | 17 |
| The automorphisms of the Heisenberg group | 19 |
| 3. | The Schrodinger representation | 21 |
| The integrated representation | 23 |
| Twisted convolution | 25 |
| The uncertainty principle | 27 |
| 4. | The Fourier-Wigner transform | 30 |
| Radar ambiguity functions | 33 |
| 5. | The Stone-von Neumann theorem | 35 |
| The group Fourier transform | 37 |
| 6. | The Fock-Bargmann representation | 39 |
| Some motivation and history | 47 |
| 7. | Hermite functions | 51 |
| 8. | The Wigner transform | 56 |
| 9. | The Laguerre connection | 63 |
| 10. | The nilmanifold representation | 68 |
| 11. | Postscripts | 73 |
| Chapter 2. | Quantization and Pseudodifferential Operators | 78 |
| 1. | The Weyl correspondence | 79 |
| Covariance properties | 83 |
| Symbol classes | 86 |
| Miscellaneous remarks and examples | 90 |
| 2. | The Kohn-Nirenberg correspondence | 93 |
| 3. | The product formula | 103 |
| 4. | Basic pseudodifferential theory | 111 |
| Wave front sets | 118 |
| 5. | The Calderon-Vaillancourt theorems | 121 |
| 6. | The sharp Garding inequality | 129 |
| 7. | The Wick and anti-Wick correspondences | 137 |
| Chapter 3. | Wave Packets and Wave Fronts | 143 |
| 1. | Wave packet expansions | 144 |
| 2. | A characterization of wave front sets | 154 |
| 3. | Analyticity and the FBI transform | 159 |
| 4. | Gabor expansions | 164 |
| Chapter 4. | The Metaplectic Representation | 170 |
| 1. | Symplectic linear algebra | 170 |
| 2. | Construction of the metaplectic representation | 177 |
| The Fock model | 180 |
| 3. | The infinitesimal representation | 185 |
| 4. | Other aspects of the metaplectic representation | 191 |
| Integral formulas | 191 |
| Irreducible subspaces | 194 |
| Dependence on Planck's constant | 195 |
| The extended metaplectic representation | 196 |
| The Groenewold-van Hove theorems | 197 |
| Some applications | 199 |
| 5. | Gaussians and the symmetric space | 200 |
| Characterizations of Gaussians | 206 |
| 6. | The disc model | 210 |
| 7. | Variants and analogues | 216 |
| Restrictions of the metaplectic representation | 216 |
| U(n,n) as a complex symplectic group | 217 |
| The spin representation | 220 |
| Chapter 5. | The Oscillator Semigroup | 223 |
| 1. | The Schrodinger model | 223 |
| The extended oscillator semigroup | 234 |
| 2. | The Hermite semigroup | 236 |
| 3. | Normalization and the Cayley transform | 239 |
| 4. | The Fock model | 246 |
| Appendix A. | Gaussian Integrals and a Lemma on Determinants | 256 |
| Appendix B. | Some Hilbert Space Results | 260 |
| Bibliography | 265 |
| Index | 275 |
Format: Paperback, 288 pages
