Application of Distributions to the Theory of Elementary Particles in Quantum Mechanics

Title page
EDITORS' PREFACE
PREFACE
1. POSITION OF THE PROBLEM
Introduction
Elements of the Theory of Distributions
Affine Spaces: Lorentz Transformations
Universal Scalar Particles
Scalar and Vector Particles in an Arbitrary Universe
Weak and Strong Convergence
2. THE SET H OF THE UNIVERSAL PARTICLES AND ITS STRUCTURE
The Space H
The Structures of H and L^_(E',E)
Scalar Particles
Tensor Products
Vector-valued Particles
Order Relations in Vector Spaces and Positivity of Antikernels
3. UNIVERSAL PARTICLES AND THE TRANSLATION INVARIANCE: KERNEL SIMPLIFICATION
Tensor Products of Distributions
Convolutions
Invariance under the Group of Translations
Fourier Transforms
Bochner's Theorem
Summary and Reduction of the Problem
The Space H for Scalar Particles
4. ELEMENTARY PARTICLES AND THE LORENTZ INVARIANCE
Elementary Particles
Supports of Extremal Measures
Mesons
Lorentz Invariant Distributions
Determination of all Mesons
Description of H for the Meson
5. SPIN PARTICLES
Vector Particles
Determination of all Vector Particles
Complete Description of F H for Vector Particles
The Electron
Vector Particles with Zero Mass
6. DEFINITION OF SOME PHYSICAL NOTIONS
Scalar Case
Vector Case
The Intrinsic Parity
APPENDIX: Density of Probability of Presence of Elementary Particles
INDEX