Theory and Applications of the Poincaré Group [E-Book] / by Y. S. Kim, Marilyn E. Noz.
Kim, Y. S., (author)
Noz, Marilyn E., (author)
Dordrecht : Springer, 1986
XV, 331 p. online resource.
englisch
9789400945586
10.1007/978-94-009-4558-6
Fundamental Theories of Physics, A New International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application ; 17
Full Text
Table of Contents:
  • I: Elements of Group Theory
  • 1. Definition of a Group
  • 2. Subgroups, Cosets, and Invariant Subgroups
  • 3. Equivalence Classes, Orbits, and Little Groups
  • 4. Representations and Representation Spaces
  • 5. Properties of Matrices
  • 6. Schur’s Lemma
  • 7. Exercises and Problems
  • II: Lie Groups and Lie Algebras
  • 1. Basic Concepts of Lie Groups
  • 2. Basic Theorems Concerning Lie Groups
  • 3. Properties of Lie Algebras
  • 4. Properties of Lie Groups
  • 5. Further Theorems of Lie Groups
  • 6. Exercises and Problems
  • III: Theory of the Poincaré Group
  • 1. Group of Lorentz Transformations
  • 2. Orbits and Little Groups of the Proper Lorentz Group
  • 3. Representations of the Poincaré Group
  • 4. Lorentz Transformations of Wave Functions
  • 5. Lorentz Transformations of Free Fields
  • 6. Discrete Symmetry Operations
  • 7. Exercises and Problems
  • IV: Theory of Spinors
  • 1. SL(2, c) as the Covering Group of the Lorentz Group
  • 2. Subgroups of SL(2, c)
  • 3. SU (2)
  • 4. 5L(2, c) Spinors and Four-Vectors
  • 5. Symmetries of the Dirac Equation
  • 6. Exercises and Problems
  • V: Covariant Harmonic Oscillator Formalism
  • 1. Covariant Harmonic Oscillator Differential Equations
  • 2. Normalizable Solutions of the Relativistic Oscillator Equation
  • 3. Irreducible Unitary Representations of the Poincaré Group
  • 4. Transformation Properties of Harmonic Oscillator Wave Functions
  • 5. Harmonic Oscillators in the Four-Dimensional Euclidean Space
  • 6. Moving O(4) Coordinate System
  • 7. Exercises and Problems
  • VI: Dirac’s Form of Relativistic Quantum Mechanics
  • 1. C-Number Time-Energy Uncertainty Relation
  • 2. Dirac’s Form of Relativistic Theory of “Atom ”
  • 3. Dirac’s Light-Cone Coordinate System
  • 4. Harmonic Oscillators in the Light-Cone Coordinate System
  • 5. Lorentz-Invariant Uncertainty Relations
  • 6. Exercises and Problems
  • VII: Massless Particles
  • 1. What is the E(2) Group?
  • 2. E(2)-like Little Group for Photons
  • 3. Transformation Properties of Photon Polarization Vectors
  • 4. Unitary Transformation of Photon Polarization Vectors
  • 5. Massless Particles with Spin 1/2
  • 6. Harmonic Oscillator Wave Functions for Massless Composite Particles
  • 7. Exercises and Problems
  • VIII: Group Contractions
  • 1. SE(2) Group as a Contraction of SO(3)
  • 2. E(2)-like Little Group as an Infinite-momentum/zero-mass Limit of the O(3)-like Little Group for Massive Particles
  • 3. Large-momentum/zero-mass Limit of the Dirac Equation
  • 4. Finite-dimensional Non-unitary Representations of the SE(2) Group
  • 5. Polarization Vectors for Massless Particles with Integer Spin
  • 6. Lorentz and Galilei Transformations
  • 7. Group Contractions and Unitary Representations of SE(2)
  • 8. Exercises and Problems
  • IX: SO(2, 1) and SU(1, 1)
  • 1. Geometry of SL(2, r) and Sp(2)
  • 2. Finite-dimensional Representations of SO(2, 1)
  • 3. Complex Angular Momentum
  • 4. Unitary Representations of SU(1, 1)
  • 5. Exercises and Problems
  • X: Homogeneous Lorentz Group
  • 1. Statement of the Problem
  • 2. Finite-dimensional Representations of the Homogeneous Lorentz Group
  • 3. Transformation Properties of Electric and Magnetic Fields
  • 4. Pseudo-unitary Representations for Dirac Spinors
  • 5. Harmonic Oscillator Wave Functions in the Lorentz Coordinate System
  • 6. Further Properties of the Homogeneous Lorentz Group
  • 7. Concluding Remarks
  • XI: Hadronic Mass Spectra
  • 1. Quark Model
  • 2. Three-particle Symmetry Classifications According to the Method of Dirac
  • 3. Construction of Symmetrized Wave Functions
  • 4. Symmetrized Products of Symmetrized Wave Functions
  • 5. Spin Wave Functions for the Three-Quark System
  • 6. Three-quark Unitary Spin and SU(6) Wave Functions
  • 7. Three-body Spatial Wave Functions
  • 8. Totally Symmetric Baryonic Wave Functions
  • 9. Baryonic Mass Spectra
  • 10. Mesons
  • 11. Exercises and Problems
  • XII: Lorentz-Dirac Deformation in High-Energy Physics
  • 1. Lorentz-Dirac Deformation of Hadronic Wave Functions
  • 2. Form Factors of Nucléons
  • 3. Calculation of the Form Factors
  • 4. Scaling Phenomenon and the Parton Picture
  • 5. Covariant Harmonic Oscillators and the Parton Picture
  • 6. Calculation of the Parton Distribution Function for the Proton
  • 7. Jet Phenomenon
  • 8. Exercises and Problems
  • References.