From Classical Mechanics to Quantum Field Theory

January 3, 2020 9:10 From Classical Mechanics to Quantum Field Theory 9in x 6in b3742-main page ix

Contents

Preface v

Acknowledgments vii

1. A Short Course on Quantum Mechanics and Methods
   of Quantization 1
   1.1 Introduction.............................. 1
   1.2 OverviewofQuantumMechanics.................. 7
   1.2.1 Fundamental definitions and examples........... 7
   1.2.2 Geometricquantummechanics............... 17
   1.3 MethodsofQuantization....................... 26
   1.3.1 Coherent states and Bargmann-Fock representation... 27
   1.3.2 Feynmanpathintegral ................... 39
   1.3.3 Weylquantization...................... 47
   Bibliography................................. 64


2. Mathematical Foundations of Quantum Mechanics: An
   Advanced Short Course 67
   2.1 Introduction: Summary of Elementary Facts of QM........ 67
   2.1.1 Physical facts about quantum mechanics......... 68
   2.1.2 Elementary formalism for the finite dimensional case... 71
   2.1.3 Timeevolution........................ 76
   2.1.4 Compositesystems ..................... 77
   2.1.5 A first look to the infinite dimensional case, CCR and
   quantizationprocedures................... 79
   2.2 Observables in Infinite Dimensional Hilbert Spaces:
   SpectralTheory............................ 85

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