Quantum Physics A Functional Integral Point of View [Paperback]

Describes fifteen years' work which has led to the construc-tion of solutions to non-linear relativistic local field e-quations in 2 and 3 space-time dimensions. Gives proof ofthe existence theorem in 2 dimensions and describes manyproperties of the solutions.Describes fifteen years' work which has led to the construc-tion of solutions to non-linear relativistic local field e-quations in 2 and 3 space-time dimensions. Gives proof ofthe existence theorem in 2 dimensions and describes manyproperties of the solutions.I An Introduction to Modern Physics.- 1 Quantum Theory.- 1.1 Overview.- 1.2 Classical Mechanics.- 1.3 Quantum Mechanics.- 1.4 Interpretation.- 1.5 The Simple Harmonic Oscillator.- 1.6 Coulomb Potentials.- 1.7 The Hydrogen Atom.- 1.8 The Need for Quantum Fields.- 2 Classical Statistical Mechanics.- 2.1 Introduction.- 2.2 The Classical Ensembles.- 2.3 The Ising Model and Lattice Fields.- 2.4 Series Expansion Methods.- 3 The Feynman-Kac Formula.- 3.1 Wiener Measure.- 3.2 The Feynman-Kac Formula.- 3.3 Uniqueness of the Ground State.- 3.4 The Renormalized Feynman-Kac Formula.- 4 Correlation Inequalities and the Lee-Yang Theorem.- 4.1 Griffiths Inequalities.- 4.2 The Infinite Volume Limit.- 4.3 ?4 Inequalities.- 4.4 The FKG Inequality.- 4.5 The Lee-Yang Theorem.- 4.6 Analyticity of the Free Energy.- 4.7 Two Component Spins.- 5 Phase Transitions and Critical Points.- 5.1 Pure and Mixed Phases.- 5.2 The Mean Field Picture.- 5.3 Symmetry, Breaking.- 5.4 The Droplet Model and Peierls Argument.- 5.5 Some Examples.- 6 Field Theory.- 6.1 Axioms.- (i) Euclidean Axioms.- (ii) Minkowski Space Axioms.- 6.2 The Free Field.- 6.3 Fock Space and Wick Ordering.- 6.4 Canonical Quantization.- 6.5 Fermions.- 6.6 Interacting Fields.- Appendix to Part I. Hilbert Space Operators and Functional Integrals.- A.1 Bounded and Unbounded Operators on Hilbert Space.- A.2 Positive Operators and Bilinear Forms.- A.3 Trace Class Operators and Nuclear Spaces.- A.4 Gaussianl³“