The course notes for this course are being continually updated and expanded. Some of them are already typed, and others (now shown as scanned hand-written notes) will be typed up very soon. The course this year (Jan-April 2016) will focus mostly on Chapters B4-B7; note that chapters B4, B6 and B7 are currently being expanded, and several new Appendices will soon appear.

Part A: PATH INTEGRAL THEORY

• A1. Introduction to path integrals.
• A2. Fluctuation determinant.
• A3. Green's functions in QM.
• A3. Correlations in QM.
• Appendix A1. Adiabatic processes in QM.
• Appendix A2. Born-Oppenheimer approximation.

Section B: Quantum Field Theory

• B1: The Generating Functional.
• B2: Fermionic Path Integrals.
• B3: Perturbation Theory and Diagrams.
• B4: Gauge Field Theory
• B5: Equations of Motion and Conservation Laws in QFT
• B6: Non-Perturbative Methods in QFT
• B7: Renormalization

Section C: Quantum Gravity and beyond

Appendix

• B1: Notes on functionals.
• B3: Diagrams for non-Relativistic Systems.
• B5: Spin Representations.
• B6: Regularization methods.