Introduction to Quantum Field Theory (Theory of Scalar Fields) - Part 2

Overview

ABOUT THE COURSE: This course, which is the second part of the course on Introduction to Quantum Field Theory (Theory of Scalar Fields) makes the connection between the Experimentally observable quantities such as cross-section and theoretically computable scattering amplitudes. Here we also discuss renormalization at one loop in phi^4 theory.INTENDED AUDIENCE: Students pursuing PhD in High Energy Physics. Advanced MSc. Physics students interested in Quantum Field Theory.PREREQUISITES: Introduction to Quantum Field Theory (Theory of Scalar Fields) - Part 1 offered by NPTEL by the same Author.

Syllabus

Week 1: Review of the basics of Scalar Field Theory coverd in QFT part-1 Week 2:The S-Matrix, Scattering Amplitude, Scattering in interacting theory Week 3:Scattering Cross-Section formula Week 4:The Kallen-Lehmann Representation. The Z factor. Week 5:Lehmann, Symanzik and Zimmermann (LSZ) reduction. Week 6:Analytic properties of functions defined through integrals. Optical theorem Week 7:Ultraviolet Divergences in Phi^4 theory and power counting, UV regularization:(a) Momentum cutoff, (b) Pauli Villars, and (c) Dimensional regularization. Week 8:Renormalization of Phi^4 theory at one loop: Renormalization of 2-pt function Week 9:Mandelstam invariants, Renormalization of 4-point function. Subtraction Schemes: MS and MS-bar schemes. Week 10:Renormalization group equations, beta functions and anomalous dimension Week 11:Solution to Callan-symanzik equations. Running coupling constant. Week 12:Fixed points: Ultra Violet and Infrared Stable fixed points. Scale invariance at fixed points. Behavious of two point function near fixed points.