## Field Theory, Especially Quantum Field Theory

*14 Feb 2004 10:55*

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