Quantum Field Theory & Critical Phenomena

Text:

J.Zinn-Justin, "Quantum Field Theory & Critical Phenomena", OUP, 2002.

      ( On-line e-book available at main library )


Mathematical Supplement


Chapter 1: Algebraic Preliminaries

  •    1.1. The Gaussian Integral       ( Apr 29, 2015 )
  •    1.2. Perturbation Theory, Connected Contributions, Steepest Descent       ( Apr 26, 2015 )
  •    1.3. Complex Structures       ( Apr 29, 2015 )
  •    1.4. Grassmann Algebras, Differential Forms       ( May 15, 2015 )
  •    1.5. Differentiation in Grassmann Algebras       ( May 17, 2015 )
  •    1.6. Integration in Grassmann Algebras       ( May 20, 2015 )
  •    1.7. Gaussian Integrals with Grassmann Variables       ( May 23, 2015 )
  •    1.8. Legendre Transformation       ( May 23, 2015 )
  •    1.9. Generating Functionals. Functional Derivatives & Determinants       ( May 23, 2015 )
  •    Chap.1.zip       ( May 23, 2015 )

    Chapter 2: Euclidean Path Integrals in Quantum Mechanics

  •    2.1. Path Integrals: The General Idea       ( May 25, 2015 )
  •    2.2. Path Integral Representation: Special Hamiltonians       ( Aug 10, 2015 )
  •    2.3. Explicit Evaluation of a Path Integral: The Harmonic Oscillator       ( Jun 05, 2015 )
  •    2.4. Partition Function. Correlation Functions       ( Jun 07, 2015 )
  •    2.5. Generating Functional of Correlation Functions. Perturbative Expansion       ( Jun 15, 2015 )
  •    2.6. Semi-Classical Expansion       ( Jun 12, 2015 )
  • Appendix A2.
  •    A2.1       ( Jun 15, 2015 )
  •    Chap.2.zip       ( Aug 10, 2015 )

    Chapter 3: Path Integrals in Quantum Mechanics: Generalizations

  •    3.1. General Hamiltonians: Phase Space Path Integral       ( Jun 16, 2015 )
  •    3.2. Hamiltonians Quadratic in Momentum Variables       ( Jun 19, 2015 )
  •    3.3. The Spectrum of the O(2) Symmetric Rigid Rotator       ( Jun 19, 2015 )
  •    3.4. The Spectrum of the O(N) Symmetric Rigid Rotator       ( Jun 28, 2015 )
  •    Properties of the n-Sphere       ( Jun 28, 2015 )
  • Appendix A3. Quantization of Spin Degrees of Freedom, Topological Actions
  •    A3.1. Symplectic Form and Quantization: General Remarks       ( Jun 24, 2015 )
  •    A3.2. Spin Dynamics & Quantization       ( Jul 01, 2015 )
  •    A3.3. The Magnetic Monopole       ( Jul 02, 2015 )
  •    Chap.3.zip       ( Jul 02, 2015 )

    Chapter 4: Stochastic Differential Equations: Langevin, Fokker-Planck Equations

  •    4.1. The Langevin Equation       ( Jul 06, 2015 )
  •    4.2. A Simple Example: The Linear Langevin Equation       ( Jul 04, 2015 )
  •    4.3. The Fokker-Planck Equation       ( Jul 11, 2015 )
  •    4.4. Equilibrium Distribution Correlation Functions       ( Jul 13, 2015 )
  •    4.5. A Special Case: The Dissipative Langevin Equation       ( Jul 10, 2015 )
  •    4.6. Path Integral Representation       ( Jul 09, 2015 )
  •    4.7. General Discretized Langevin Equation       ( Jul 10, 2015 )
  •    4.8. Brownian Motion on Riemannian Manifolds       ( Jul 16, 2015 )
  • Appendix A4. Discrete Markov Stochastic Processes: A Few Remarks
  •    A4.1. The Spectrum of the Transition Matrix       ( Jul 20, 2015 )
  •    A4.2. Detailed Balance       ( Jul 21, 2015 )
  •    A4.3. Stochastic Process with Prescribed Equilibrium Distribution       ( Jul 21, 2015 )
  •    Chap.4.zip       ( Jul 21, 2015 )

    Chapter 5: Path & Functional Integrals in Quantum Statistical Physics

  •    5.1. Quantum Mechanics: Holomorphic Formalism       ( Aug 04, 2015 )
  •    5.2. Holomorphic Path Integral       ( Aug 21, 2015 )
  •    5.3. Path Integrals with Fermions       ( Aug 03, 2015 )
  •    5.4. Quantum Statistical Physics: Fixed Number of Particles       ( Aug 10, 2015 )
  •    5.5. The Bose Gas: Functional Integrals       ( Aug 23, 2015 )
  •    5.6. The Fermi Gas: Functional Integrals       ( Aug 23, 2015 )
  •    Fourier Transforms       ( Oct 10, 2014 )
  •    Chap.5.zip       ( Aug 23, 2015 )

    Chapter 6: Quantum Evolution: From Particles to Fields

  •    6.1. Time Evolution & Scattering Matrix in Quantum Mechanics       ( Aug 10, 2015 )
  •    6.2. Path Integral & S-Matrix: Perturbation Theory       ( Aug 14, 2015 )
  •    6.3. Path Integral & S-Matrix: Semi-Classical Expansions       ( Aug 19, 2015 )
  •    6.4. S-Matrix & Holomorphic Formalism       ( Aug 24, 2015 )
  •    6.5. Fermi Gas: Evolution Operator       ( Aug 24, 2015 )
  •    6.6. Relativistic Quantum Field Theory: The Scalar Field       ( Aug 28, 2015 )
  •    Chap.6.zip       ( Aug 28, 2015 )

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