Quantum Theory, Groups and Representations: An Introduction

Front Matter ....Pages i-xxii
 Introduction and Overview  (Peter Woit)....Pages 1-14
 The Group U(1) and its Representations  (Peter Woit)....Pages 15-26
 Two-state Systems and SU(2)  (Peter Woit)....Pages 27-37
 Linear Algebra Review, Unitary and Orthogonal Groups  (Peter Woit)....Pages 39-53
 Lie Algebras and Lie Algebra Representations  (Peter Woit)....Pages 55-71
 The Rotation and Spin Groups in Three and Four Dimensions   (Peter Woit)....Pages 73-86
 Rotations and the Spin \(\frac{1}{2}\) Particle in a Magnetic Field  (Peter Woit)....Pages 87-101
 Representations of SU(2) and SO(3)  (Peter Woit)....Pages 103-124
 Tensor Products, Entanglement, and Addition of Spin  (Peter Woit)....Pages 125-138
 Momentum and the Free Particle  (Peter Woit)....Pages 139-147
 Fourier Analysis and the Free Particle  (Peter Woit)....Pages 149-164
 Position and the Free Particle  (Peter Woit)....Pages 165-180
 The Heisenberg group and the Schrödinger Representation  (Peter Woit)....Pages 181-188
 The Poisson Bracket and Symplectic Geometry  (Peter Woit)....Pages 189-198
 Hamiltonian Vector Fields and the Moment Map  (Peter Woit)....Pages 199-214
 Quadratic Polynomials and the Symplectic Group  (Peter Woit)....Pages 215-227
 Quantization  (Peter Woit)....Pages 229-236
 Semi-direct Products  (Peter Woit)....Pages 237-243
 The Quantum Free Particle as a Representation of the Euclidean Group  (Peter Woit)....Pages 245-257
 Representations of Semi-direct Products  (Peter Woit)....Pages 259-273
 Central Potentials and the Hydrogen Atom  (Peter Woit)....Pages 275-285
 The Harmonic Oscillator  (Peter Woit)....Pages 287-298
 Coherent States and the Propagator for the Harmonic Oscillator  (Peter Woit)....Pages 299-311
 The Metaplectic Representation and Annihilation and Creation Operators, \(d=1\)  (Peter Woit)....Pages 313-324
 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d  (Peter Woit)....Pages 325-339
 Complex Structures and Quantization  (Peter Woit)....Pages 341-356
 The Fermionic Oscillator  (Peter Woit)....Pages 357-363
 Weyl and Clifford Algebras  (Peter Woit)....Pages 365-372
 Clifford Algebras and Geometry  (Peter Woit)....Pages 373-381
 Anticommuting Variables and Pseudo-classical Mechanics  (Peter Woit)....Pages 383-393
 Fermionic Quantization and Spinors  (Peter Woit)....Pages 395-410
 A Summary: Parallels Between Bosonic and Fermionic Quantization  (Peter Woit)....Pages 411-412
 Supersymmetry, Some Simple Examples  (Peter Woit)....Pages 413-420
 The Pauli Equation and the Dirac Operator  (Peter Woit)....Pages 421-431
 Lagrangian Methods and the Path Integral  (Peter Woit)....Pages 433-445
 Multiparticle Systems: Momentum Space Description  (Peter Woit)....Pages 447-463
 Multiparticle Systems and Field Quantization  (Peter Woit)....Pages 465-475
 Symmetries and Non-relativistic Quantum Fields  (Peter Woit)....Pages 477-491
 Quantization of Infinite dimensional Phase Spaces  (Peter Woit)....Pages 493-501
 Minkowski Space and the Lorentz Group  (Peter Woit)....Pages 503-513
 Representations of the Lorentz Group  (Peter Woit)....Pages 515-525
 The Poincaré Group and its Representations  (Peter Woit)....Pages 527-539
 The Klein–Gordon Equation and Scalar Quantum Fields  (Peter Woit)....Pages 541-559
 Symmetries and Relativistic Scalar Quantum Fields  (Peter Woit)....Pages 561-572
 U(1) Gauge Symmetry and Electromagnetic Fields  (Peter Woit)....Pages 573-583
 Quantization of the Electromagnetic Field: the Photon  (Peter Woit)....Pages 585-603
 The Dirac Equation and Spin \(\frac{1}{2}\) Fields  (Peter Woit)....Pages 605-620
 An Introduction to the Standard Model  (Peter Woit)....Pages 621-626
 Further Topics  (Peter Woit)....Pages 627-629
Back Matter ....Pages 631-668