Quantum Theory, Groups and Representations An Introduction /
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics cou...
| Κύριος συγγραφέας: | |
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| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
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| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Preface
- 1 Introduction and Overview
- 2 The Group U(1) and its Representations
- 3 Two-state Systems and SU(2)
- 4 Linear Algebra Review, Unitary and Orthogonal Groups
- 5 Lie Algebras and Lie Algebra Representations
- 6 The Rotation and Spin Groups in 3 and 4 Dimensions
- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field
- 8 Representations of SU(2) and SO(3)
- 9 Tensor Products, Entanglement, and Addition of Spin
- 10 Momentum and the Free Particle
- 11 Fourier Analysis and the Free Particle
- 12 Position and the Free Particle
- 13 The Heisenberg group and the Schrödinger Representation
- 14 The Poisson Bracket and Symplectic Geometry
- 15 Hamiltonian Vector Fields and the Moment Map
- 16 Quadratic Polynomials and the Symplectic Group
- 17 Quantization
- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group
- 20 Representations of Semi-direct Products
- 21 Central Potentials and the Hydrogen Atom
- 22 The Harmonic Oscillator
- 23 Coherent States and the Propagator for the Harmonic Oscillator
- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1
- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d
- 26 Complex Structures and Quantization
- 27 The Fermionic Oscillator
- 28 Weyl and Clifford Algebras
- 29 Clifford Algebras and Geometry
- 30 Anticommuting Variables and Pseudo-classical Mechanics
- 31 Fermionic Quantization and Spinors
- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization
- 33 Supersymmetry, Some Simple Examples
- 34 The Pauli Equation and the Dirac Operator
- 35 Lagrangian Methods and the Path Integral
- 36 Multi-particle Systems: Momentum Space Description
- 37 Multi-particle Systems and Field Quantization
- 38 Symmetries and Non-relativistic Quantum Fields
- 39 Quantization of Infinite dimensional Phase Spaces
- 40 Minkowski Space and the Lorentz Group
- 41 Representations of the Lorentz Group
- 42 The Poincaré Group and its Representations
- 43 The Klein-Gordon Equation and Scalar Quantum Fields
- 44 Symmetries and Relativistic Scalar Quantum Fields
- 45 U(1) Gauge Symmetry and Electromagnetic Field
- 46 Quantization of the Electromagnetic Field: the Photon
- 47 The Dirac Equation and Spin-1/2 Fields
- 48 An Introduction to the Standard Model
- 49 Further Topics
- A Conventions
- B Exercises
- Index.
