Author | Yndurรกin, Francisco J. author |
---|---|
Title | Relativistic Quantum Mechanics and Introduction to Field Theory [electronic resource] / by Francisco J. Yndurรกin |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1996 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61057-8 |
Descript | XII, 332 p. online resource |
1. Relativistic Transformations. The Lorentz Group -- 1.1 Rotations, and Space and Time Reversal for Particles with Spin -- 1.2 Galilean Transformations -- 1.3 Lorentz Transformations. Normal Parameters -- 1.4 Minkowski Space. The Full Lorentz Group -- 1.5 The Lorentz Group -- 1.6 Geometry of Minkowski Space -- 1.7 Transformation Properties of Physical Quantities Under the Lorentz Group -- 1.8 Covariant Form of the Maxwell Equations -- 1.9 Minkowski Space: Metric, Conventions -- 2. The KleinโGordon Equation. Relativistic Equation for Spinless Particles -- 2.1 The KleinโGordon Equation. Generalities -- 2.2 Wave Equation for Free Spinless Particles -- 2.3 Plane Waves. Current. Scalar Product -- 2.4 Interaction with the Classical Electromagnetic Field. Gauge Invariance -- 2.5 Particle in a Coulomb Field -- 3. Spin 1/2 Particles -- 3.1 The Dirac Equation -- 3.2 Invariance Properties of the Dirac Equation -- 3.2.1 Rotations -- 3.2.2 Boosts -- 3.2.3 Parity -- 3.2.4 Time Reversal -- 3.3 Density of Particles. Current. Scalar Product -- 3.4 Minimal Replacement. Gauge Invariance. Large and Small Components: Nonrelativistic Limit of the Dirac Equation... -- 3.5 Plane Waves. States with Weil-Defined Spin -- 3.6 Radial Form of the Dirac Equation. Free-Particle Solutions -- 3.6.1 Radial Form of H -- 3.6.2 Free Particles -- 3.7 The Problem of Negative Energies in the Dirac Equation. The Dirac Sea. Hole Theory. Charge Conjugation -- 3.7.1 Negative Energies. The Dirac Sea. Holes -- 3.7.2 Charge Conjugation -- 3.8 Covariants and Projectors -- 3.8.1 Covariants -- 3.8.2 Projectors -- 3.9 Massless Spin 1/2 Particles -- 4. Dirac Particle in a Potential -- 4.1 Dirac Particle in a Spherical Well -- 4.2 Particle in a Coulomb Potential: Continuum States -- 4.3 Scattering States. Phase Shifts. Cross-sections. Wave Function at the Origin -- 4.3.1 Scattering States. Phase Shifts -- 4.3.2 Cross-sections -- 4.3.3 Wave Function at the Origin -- 4.4 Bound States in a Coulomb Potential -- 4.5 Semirelativistic Approximation: the FoldyโWouthuysen Transformation -- 4.5.1 General Method -- 4.5.2 Electromagnetic Interactions -- 4.5.3 Free Particle -- 5. Massive Particles with Spin 1. Massless Spin 1 Particle: Photon Wave Functions. Particles with Higher Spins (3/2, 2,โฆ) -- 5.1 Particle with Spin 1 and Mass m ? 0 -- 5.2 Particle with Spin 1 and Zero Mass: The Photon. Plane Waves. Photon Spin -- 5.2.1 Photon Wave Function. Gauge Fixing. Transformation Properties -- 5.2.2 Plane Waves. Helicity States -- 5.2.3 Field Variables as Wave Functions for the Photon. The Schwinger Gauge -- 5.3 Angular Momentum Eigenstates for the Photon. Vector Spherical Harmonics. Multipoles -- 5.3.1 General Useful Formulas -- 5.3.2 Multipoles -- 5.3.3 Photon Wave Functions with Well-Defined Angular Momentum -- 5.4 Particles with Higher Spins. RaritaโSchwinger and BargmannโWigner Equations. The Graviton -- 5.4.1 RaritaโSchwinger Equations -- 5.4.2 BargmannโWigner Equations -- 5.4.3 The Graviton -- 6. General Description of Relativistic States -- 6.1 Preliminaries -- 6.2 Relativistic One-Particle States: General Description -- 6.3 Relativistic States of Massive (m?0) Particles -- 6.4 Massless Particles -- 6.5 Many-Particle States. CreationโAnnihilation Operators. Fock Space -- 6.6 Connection with the Wave Function Formalism -- 7. General Description of Relativistic Collisions: S Matrix, Cross-sections and Decay Rates. Partial Wave Analyses -- 7.1 Two-Particle States. Separation of the Centre of Mass Motion. States with Weil-Defined Angular Momentum -- 7.2 Kinematics of Two-Particle Collisions -- 7.3 The S Matrix. Scattering Amplitude. Nonrelativistic Limit -- 7.4 Cross-sections and Decay Rates. The Optical Theorem -- 7.5 Partial Wave Analysis and Phase Shifts. I. Spinless Elastic Scattering. Effective Range Expansion... -- 7.5.1 Partial Wave Analysis -- 7.5.2 Effective Range Formalism -- 7.6 Partial Wave Analysis. II. Several Two-Body Channels -- 7.6.1 Multichannel Analysis -- 7.6.2 Effective Range Approximation -- 7.7 Partial Wave Analysis. III. Particles with Spin -- 7.7.1 Spin Analysis -- 7.7.2 Scattering of Spin 0 - Spin 1/2 Particles -- 7.8 Evaluation of the S Matrix -- 7.8.1 The S Matrix and the Interaction Picture -- 7.8.2 The S Matrix in the Lippmann-Schwinger Formalism. -- 7.8.3 Scattering by Two Interactions -- 8. Quantization of the Electromagnetic Field. Interaction of Radiation with Matter -- 8.1 Normal, or Wick, Products -- 8.2 Quantization of the Electromagnetic Field (Coulomb Gauge). The Casimir Effect -- 8.2.1 Quantization of the Electromagnetic Field -- 8.2.2 Multipole Expansion -- 8.2.3 The Casimir Effect -- 8.3 Interaction of the Radiation with Slowly Moving Particles... -- 8.3.1 Radiative Decays, and Absorption of Radiation -- 8.3.2 Low-Energy Compton Scattering -- 8.4 Bremsstrahlung -- 8.5 The Classical Limit. Coherent States -- 8.6 Uncertainty Relations for Field Variables -- 9. Quantum Fields: Spin 0, 1/2, 1. Covariant Quantization of the Electromagnetic Field -- 9.1 Generalities -- 9.2 Localization of Particles in Relativistic Quantum Mechanics. -- 9.3 Retardation and Consistency -- 9.4 Quantization of Scalar Fields and of Massive Vector Fields... -- 9.4.1 Second Quantization for Spinless Particles -- 9.4.2 Massive Vector Particles -- 9.5 Quantization of the Dirac Field. Weyl and Majorana Particles -- 9.6 Covariant Quantization of the Electromagnetic Field -- 9.6.1 The Gupta-Bleuler Space -- 9.6.2 Covariant Transformation -- 9.6.3 The Metric Operator Method -- 9.7 Time-Ordered Product. Propagators -- 9.8 Interactions in Quantum Field Theory. Lagrangian Formulation -- 9.8.1 Lagrangian Formalism for Fields -- 9.8.2 Interactions -- 9.9 Gauge Invariance in Quantum Electrodynamics -- 10. Interactions in Quantum Field Theory. Nonrelativistic Limit. Reduction to Equivalent Potential -- 10.1 Potentials Equivalent to Field-Theoretic Interactions. General Method -- 10.2 Equivalent Potential for Two Particles in Electromagnetic Interaction -- 10.2.1 Elastic Collision of Two Charged Particles in the Born Approximation -- 10.2.2 Nonrelativistic Limit -- 10.2.3 Relativistic Corrections. The Breit Term -- 10.3 Hydrogenlike Atoms: Hyperfine Structure. System with Two Electrons: the Helium Atom -- 10.3.1 Hydrogenlike Atoms -- 10.3.2 System With Two Electrons. The Helium Atom -- 10.4 Electron-Positron Collisions: Effective Potential. Positronium -- 10.4.1 Scattering Amplitude in the Born Approximation. -- 10.4.2 Annihilation Channel -- 10.4.3 Positronium -- 10.5 Scalar and Pseudoscalar Interactions. The Yukawa Potential. -- 10.6 Weak Neutral Currents. Parity Violation in Atoms -- 11. Relativistic Collisions in Field Theory. Feynman Rules. Decays -- 11.1 Electron-Positron Annihilation into Two Photons, and Pair Creation by Two-Photon Collisions -- 11.1.1 e+e- Annihilation into 2? -- 11.1.2 Creation of an e+e- Pair by Two Photons -- 11.2 Feynman Rules. Gauge Invariance -- 11.2.1 Feynman Rules for the Evaluation of Transition Amplitudes -- 11.2.2 Gauge Invariance -- 11.3 Polarized and Unpolarized Cross-sections. Sums Over Polarizations -- 11.4 Compton Scattering (Relativistic) -- 11.5 Decay of Bound States -- 11.5.1 General Theory -- 11.5.2 Decays of Positronium -- 11.5.3 Decay of Muonium into e+e-. Decays of Quarkonium -- 12. Relativistic Interactions with Classical Sources -- 12.1 Interaction with a Fixed (Classical) Potential -- 12.1.1 Scattering by an External Field -- 12.1.2 Bremsstrahlung -- 12.2 Photon Emission by a Classical Source. The Bloch-Nordsieck Theorem. Classical Limit -- 12.2.1 Classical Radiation -- 12.2.2 Photon Emission by a Classical Current -- 12.2.3 Radiation of Coherent States -- 12.2.4 The BlochโNordsieck Theorem -- 12.3 Propagation of an Electron in a Classical Potential. The Proper-Time Method -- 12.3.1 Electron in a Coulomb Potential -- 12.3.2 The Proper-Time Method -- 12.3.3 Dirac Particle in a Constant Field, or in a Plane Wave -- Appendices -- A.1 Spherical Harmonics, ClebschโGordan Coefficients, Matrix Representations of the Rotation Group -- A.1.1 Spherical Harmonics -- A.1.2 Some Specific Values -- A.1.3 Multiplication Formulas -- A.1.4 Gegenbauer-like Formulas -- A.1.5 Spinor and Vector Spherical Harmonics -- A.1.6 ClebschโGordan Coefficients -- A.1.7 Rotation Matrices -- A.2 Special Functions -- A.2.1 Kummer, or Confluent Hypergeometric Functions -- A.2.2 Bessel Functions -- A.2.3 Spherical Bessel Functions -- A.2.4 Bessel Functions of the Second Kind -- A.2.5 Laguerre Polynomials -- A.4 ? Matrices -- A.4.1 The Pauli Realization -- A.4.2 The Weyl Realization -- A.4.3 The Majorana Realization -- A.6 Physical Quantities -- A.6.1 SI (Gauss) Units -- A.6.3 Other Relations -- References