Field Theory, Especially Quantum Field Theory

Last update: 14 Feb 2004 10:55
First version:

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Yet another inadequate placeholder

So long as I am using these notebooks to play the Humiliation Game, I might as well confess that I feel like I understand perturbation theory and Feynman diagrams at a fairly intuitive level, I do not have the same feeling of understanding about renormalization. I can do it, but I don't get it --- or, rather, I could when I was in graduate school in the 1990s, taking classes in QFT and studying to do particle-physics phenomonology, and even then I didn't have a feeling for it. (I am much happier having found different areas to work in.) Reading Talagrand, a quarter of a century after graduate school, makes me feel a little better about this, but only a little.

See also:
• Cumulants, and Cumulant Generating Functions
• Path Integrals and Feynman Diagrams for Classical Stochastic Processes

Recommended, non-technical, big picture:
• Richard Feynman, QED: The Strange Theory of Light and Matter

Recommended, somewhat technical, big picture:
• David Griffith, Elementary Particles [Contains an absolutely painless introduction to Feynman diagrams, and is generally a treasure.]
• Richard D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem
• Paul Teller, An Interpretive Introduction to Quantum Field Theory
• Steven Weinberg, "What is Quantum Field Theory, and What Did We Think It Is?", hep-th/9702027

Recommended, harder, big picture:
• Ian Lawrie, A Unified Grand Tour of Theoretical Physics [Very good on the general structure of physical theory, and why field theories are so sensible and useful. Review: Bon Voyage!]
• J. J. Sakurai, Advanced Quantum Mechanics
• R. F. Streater and A. S. Wrightman, PCT, Spin and Statistics, and All That
• Michel Talagrand, What Is a Quantum Field Theory? A First Introduction for Mathematicians
• Steven Weinberg, The Quantum Theory of Fields, I and II

Recommended, harder, close-ups:
• Peter beim Graben and Harald Atmanspacher, "Complementarity in Classical Dynamical Systems", nlin.CD/0407046 [Symbolic dynamics approached in the framework of algebraic QFT]
• Kirill Ilinski, Physics of Finance: Gauge Modelling in Non-equilibrium Pricing [Tries to derive results in financial economics from field-theoretic methods. Does not claim that the stock market follows directly from field theory. Makes a surprising amount of sense. Review: Gauge Connections for Fun and (More Importantly) Profit]
• Eric Mjolsness, "Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview", cs.AI/0511073 [The semantics involves the formalism of quantum field theory!]
• Michael Nielsen, Introduction to Yang-Mills theories
• Silvan S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga [A long, technical history of the most successful of the field theories, quantum electrodynamics, from the late '20s through the '50s, with a little about later developments in field theory. It's a tour de force, but to really follow it you need to know the theory already.]
• Eric Smith, "Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions", arxiv:1102.3938

To read, historical and philosophical:
• Laurie Brown, Renormalization: From Lorentz to Landau and Beyond [History of renormalization methods]
• James Robert Brown (ed.), "Special Issue on Feynman Diagrams", Perspectives on Science 26:4 (August 2018)
• Tian Yu Cao, Conceptual Developments of Twentieth Century Field Theories
• Elena Castellani, "Reductionism, Emergence, and Effective Field Theories," physics/0101039
• David Kaiser, Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics
• David Kaiser, Kenji Ito and Karl Hall, "Spreading the Tools of Theory: Feynman Diagrams in the USA, Japan, and the Soviet Union", Social Studies of Science 34 (2004): 879--922 [JSTOR]

To read, historical interest:
• F. J. Dyson, "The Radiation Theories of Tomonaga, Schwinger, and Feynman", Physical Review 75 (1949): 486

To read, technical:
• Jan Ambjorn et al., Quantum Geometry: A Statistical Field Theory Approach
• Jean-Michel Caillol, Oksana Patsahan, and Ihor Mryglod, "Statistical field theory for simple fluids: the collective variables representation", cond-mat/0503213
• Predrag Cvitanović
  • Field Theory (1983)
  • Quantum Field Theory: A Cyclist Tour (2005?)
• Xavier Gr´cia, Miguel C. Munoz-Lecanda, Narciso Roman-Roy, "On some aspects of the geometry of differential equations in physics", math-ph/0402030
• Hans Halvorson and Michael Mueger, "Algebraic Quantum Field Theory", math-ph/0602036 [202 pp. review "article"]
• Alex Kamenev, Field Theory of Non-Equilibrium Systems
• Le Bellac, Thermal Field Theory
• Alexandre Lefevre, Giulio Biroli, "Dynamics of interacting particle systems: stochastic process and field theory", arxiv:0709.1325
• Istvan Montvay and Gernot Munster, Quantum Fields on a Lattice
• Michael E. Peskin, An Introduction To Quantum Field Theory
• Michael Polyak, "Feynman diagrams for pedestrians and mathematicians", math.GT/0406251
• Jorgen Rammer, Quantum Field Theory of Non-equilibrium States
• Uwe C. Tauber, "Field Theory Approaches to Nonequilibrium Dynamics", cond-mat/0511743
• David J. Toms, The Schwinger Action Principle and Effective Action
• Wald, Quantum Field Theory in Curved Spacetime
• Weinberg
  • "Effective Field Theory, Past and Future", arxiv:0908.1964
  • QFT vol. II, Modern Applications
• F. W. Wiegal, Introduction to Path-Integral Methods
• Andreas Wipf, Statistical Approach to Quantum Field Theory
• Ji-Feng Yang, "Renormalization group equations as 'decoupling' theorems", hep-th/0507024
• A. Zee
  • Quantum Field Theory in a Nutshell
  • Quantum Field Theory, as Simply as Possible

Notebooks :