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 
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
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
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
Nonequilibrium Quantum Field Theory
This PDF book covers the following topics related to Non-equilibrium Quantum Field Theory : Fundamentals of Nonequilibrium Statistical Mechanics, Basics of Nonequilibrium Quantum Field Theory, Gauge Invariance, Dissipation, Entropy, Noise and Decoherence, Thermal, Kinetic and Hydrodynamic Regimes, Applications to Selected Current Research.
Author(s): Esteban A. Calzetta, University of Buenos Aires and Conicet, Bei-lok B. Hu, University of Maryland
554 Pages
Introduction to Gauge Field Theory
This book online covers the following topics related to Introduction to Gauge Field Theory : Path integrals, Path integrals in non-relativistic quantum mechanics, Classical field theory, Quantum field theory of a scalar field, Scattering amplitudes, Feynman rules for kcp* theory, Renormalisation of X(p4 theory, Quantum field theory with fermions, Gauge field theories, Feynman rules for quantum chromodynamics, Renormalisation of q c d and q e d at one-loop order, q c d and asymptotic freedom, Spontaneous symmetry breaking, Feynman rules for electroweak theory, Renormalisation of electroweak theory, Grand unified theory, Field theories at finite temperature.
Author(s): David Bailin, Alexander Love
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
