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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