


Chapter I SPINORS AND TENSORS 1. The Lorentz Group The Minkowski metric Lorentz transformations 2. The Eestricted Lorentz Group and the Infinitesimal Lorentz Trans formations A theorem Special Lorentz group Restricted transformations Infinitesimal transformations 3. Vector Spaces [Fields] and Representations Representations of the Lorentz group Equivalent representations Infinitesimal transformations 4. The TJnimodular Group c2 and its Representations Unimodular transformations Representations of the group e2 6. The Connexion between the Group c2 and the Lorentz Group Representations of the restricted Lorentz group Representations of the full Lorentz group Tensors 6. The Connexion between Tensors and Spinors [or Bispinors] The connexion between fourvectors and spinors The connexion between tensors and spinors Invariant relations between tensors and spinors 7. Spinor and Tensor Analysis Differential operations Invariant differential equations Invariant integration processes World lines 8. Inversions of Space and Time and their Twocomponent Represen tations Various types of tensors Various types of spinors Twocomponent representations Invariant equations and the determination of a Connexions between the various types of ymatrices Bilinear forms Twocomponent equations Chapter II VARIATIONAL PRINCIPLES 1. The General Variational Principle for Fields The action functional Variational formalism The principle of stationary action 2. Integral Conservation Laws Gauge transformations of the first kind Translations and rotations The functional F[o] Integral conservation laws 3. Verification of the Integral Conservation Laws Necessary and sufficient conditions for the conservation laws Discussion The local case 4. Differential Conservation Laws The nonlocal case Interpretation The local case Canonical transformations 5. The General Variational Principle for one Independent Variable The action functional The first variation of the action functional The equations of motion Invariance with respect to parametrization Integral conservation laws Differential conservation laws Chapter III EXAMPLES 1. NonInteracting Fields. Neutral and Complex Scalar Fields Neutral scalar field, variational principle, field equations and conservation laws Solutions of the field equations The. initial value problem Complex scalar field 2. NonInteracting Fields. The First Rank Bispinor Field Variational principle, field equations and conservation laws Solutions of the field equations The initial value problem 3. NonInteracting Fields. Vector, PseudoVector and PseudoScalar Fields Vector field Pseudoscalar and pseudovector field 4. External Interactions. Scalar [or PseudoScalar] Field Interaction with external sources Solutions of the inhomogeneous equations Interaction with external fields Solutions of the perturbed equations An equivalence theorem 6. External Interactions. Bispinor Field Interaction with external sources Solutions of the inhomogeneous equations Interaction with external fields Solutions of tho perturbed equations An equivalence theorem 6. Mutually Interacting Fields. Electromagnetic Field in Interaction with the Electron Field The action functional Gauge invariance of the second kind Energymomentum Solutions of the field equations 7. Fokker's Variational Principle Action functional and equations of motion Field equations The subsidiary condition The potentials of Lienard and Wiechert The procedure of Wheeler and Feynman Modified interactions Selfaction Radiation damping Conservation laws Solutions of the equations of motion 8. NonLocal Interactions Action functional The local limit Field equations and conservation laws Solutions of the field equations Mass eigenvalue problem 9. Example of a NonLinear Theory The action functional and the field equations Static solutions Energymomentum Chapter rv THE BASIC SOLUTIONS OP THE FIELD EQUATIONS 1. Introduction of Various Types of deltaFunctions Homogeneous KleinGordon equation. The functions delta and delta(1) The functions delta(+) and delta() Integral relations Inhomogeneous equation. The function delta The functions deltaret, deltaadv and deltaF Further integral relations The homogeneous and inhomogeneous Dirac equations. The Sfunctions 2. Fourier Transforms of the delta and SFunctions Threedimensional Fourier transforms Fourdimensional Fourier transforms 3. Explicit Calculation of the deltaFunctions The function delta The function delta(1) Absolute integrability 4. Representation of the deltaFunctions by Integrals in the Complex kPlane 