Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics. Patrick Muldowney
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Table of Contents
1 Cover
4 Preface
5 Reading this BooknotesSet Note
7
Part I: Stochastic Calculus
Chapter 1: Stochastic Integration
Notes
Chapter 2: Random Variation
2.1 What is Random Variation?
2.2 Probability and Riemann Sums
2.3 A Basic Stochastic Integral
2.4 Choosing a Sample Space
2.5 More on Basic Stochastic Integral
Notes
Chapter 3: Integration and Probability
3.1 ‐Complete Integration
3.2 Burkill‐complete Stochastic Integral
3.3 The Henstock Integral
3.4 Riemann Approach to Random Variation
3.5 Riemann Approach to Stochastic Integrals
Notes
Chapter 4: Stochastic Processes
4.1 From
8
Part II: Field Theory
Chapter 7: Gauges for Product Spaces
7.1 Introduction
7.2 Three‐dimensional Brownian Motion
7.3 A Structured Cartesian Product Space
7.4 Gauges for Product Spaces
7.5 Gauges for Infinite‐dimensional Spaces
7.6 Higher‐dimensional Brownian Motion
7.7 Infinite Products of Infinite Products
Notes
Chapter 8: Quantum Field Theory
8.1 Overview of Feynman Integrals
8.2 Path Integral for Particle Motion
8.3 Action Waves
8.4 Interpretation of Action Waves
8.5 Calculus of Variations
8.6 Integration Issues