Lectures on effective field theory

Field Theory Notes by Pete L Clark

This note describes introduction to fields, Some examples of fields, Field extensions, Normal extensions, Separable algebraic extensions, Norms, Traces and discriminants, The primitive element theorem, Galois extensions, Solvable extensions, Computing galois groups, Structure of transcendental extensions, Linear disjointness, Derivations and differentials and ordered field.

Author(s): Pete L Clark

167 Pages

Fields and Galois Theory

This note on fields and Galois theory explains the following topics: Basic Definitions and Results, Splitting Fields Multiple Roots, The Fundamental Theorem of Galois Theory, Computing Galois Groups, Applications of Galois Theory, Algebraic Closures, Infinite Galois Extensions, The Galois theory of tale algebras and Transcendental Extensions.

Author(s): J.S.Milne

144 Pages

Class Field Theory

This note covers Local Class Field Theory Lubin Tate Theory, The Cohomology of Groups, Local Class Field Theory Cohomology, Brauer Groups, Global Class Field Theory Statements, L Series and the Density of Primes, Global Class Field Theory Proofs and Complements.

Author(s): J.S.Milne

296 Pages

A Course in Field Theory by Pierre van Baal

This page online covers the following topics related to Field Theory : Quantisation of Fields, Euler–Lagrange Equations, Tree-Level Diagrams, Hamiltonian Perturbation Theory, Path Integrals in Quantum Mechanics, Path Integrals in Field Theory, Perturbative Expansion in Field Theory, he Scattering Matrix, Cross Sections, Decay Rates, The Dirac Equation, Plane Wave Solutions of the Dirac Equation, The Dirac Hamiltonian, Path Integrals for Fermions, Feynman Rules for Vector Fields, Quantum Electrodynamics—QED, Non-Abelian Gauge Theories, The Higgs Mechanism, Gauge Fixing and Ghosts, The Standard Model, Loop Corrections and Renormalisation.

Author(s): Pierre van Baal

NA Pages

David Tong Lectures on Statistical Field Theory

The content in this site are as follows : From Spins to Fields, The Ising Model, Landau Mean Field Theory, Universality, Critical Exponents, Landau-Ginzburg Theory, Domain Walls, The Lower Critical Dimension, My First Path Integral, The Thermodynamic Free Energy (again); Correlation Functions, Correlation Length; The Upper Critical Dimension, The Analogy with Quantum Field Theory, The Renormalisation Group, The Big Idea, Universality Explained, Scaling Explained; Relevant, Irrelevant and Marginal; The Gaussian Fixed Point, Dangerously Irrelevant Operators, Interactions, Feynman Diagrams; the Epsilon Expansion, the Wilson-Fisher Fixed Point, A Sniff of Conformal Symmetry, Continuous Symmetry, The Importance of Symmetry, O(N) Models, Goldstone Bosons and Goldstone's Theorem, The Mermin-Wagner Theorem; Sigma Models, Background Fields, Large N, the Kosterlitz-Thouless Transition, Vortices, the Coulomb Gas, the Sine-Gordon Model, RG for KT and SG.

Author(s): David Tong, University of Cambridge

NA Pages

QFT Lectures Notes by Jared Kaplan

The contents of this lecture notes are : Useful References and Texts, Philosophy, Review of Lagrangians and Harmonic Oscillators, Balls and Springs, Free Scalar Quantum Field Theory with Special Relativity, Interactions in Classical Field Theory with a View Towards QFT, Overview of Scattering and Perturbation Theory, Old Fashioned Perturbation Theory, Feynman Rules as a Generalization of Classical Physics, The Hamiltonian Formalism for Perturbation Theory, Feynman Rules from the Hamiltonian Formalism, Particles with Spin, Covariant Derivatives and Scalar QED, Scattering and Ward Identities in Scalar QED, Spinors and QED, Quantization and Feynman Rules for QED, Casimir Effect, The Exact pt Correlator Kallen-Lehmann Representation, Large Logarithms and Renormalization Flows, QM Example of Wilsonian Renormalization, Wilsonian Renormalization Flows, Path Integrals, Path Integrals and Statistical Physics, Discrete Symmetries and Spinors, More on Spin and Statistics, QED Vacuum Polarization and Anomalous Magnetic Moment, Renormalization and QED, IR Divergences and Long Wavelength Physics, Implications of Unitarity, Interlude on Lie Groups and Lie Algebras, Overview of Lie Algebra Classi cation and Representations, Spontaneously Broken Global Symmetries and Goldstone Bosons, Renormalization in YM and Asymptotic Freedom, Higgs Mechanism, Parton Model and Deep Inelastic Scattering, Anomalies as Almost Local E ects, A Lecture on Cosmological Perturbation Theory.

Author(s): Jared Kaplan, Department of Physics and Astronomy, Johns Hopkins University

260 Pages