Quantum field theory
Introductory
Srednicki, Quantum field theory
Schwartz, Quantum field theory and the standard model
Comprehensive
Weinberg, The quantum theory of fields, vols 1 & 2
Itzikson and Zuber, Quantum field theory
Zinn-Justin, Quantum Field Theory and Critical Phenomena
Ziedler, Quantum field theory, vols 1-3
Mathematical
Chatterjee, Introduction to quantum field theory for mathematicians
Fradkin, Quantum field theory: an integrated approach
Folland, Quantum field theory: a tourist guide for mathematicians
Ticciati, Quantum field theory for mathematicians
Talagrand, What is a quantum field theory ?
Faria and Melo, Mathematical Aspects of Quantum Field Theory
Bogolubov et al, General Principles of Quantum Field Theory
Causal perturbation theory (Epstein-Glaser)
Scharf, Finite Quantum Electrodynamics: The Causal Approach
Scharf, Gauge Field Theories: Spin One and Spin Two
Axiomatic QFT
Wightman and Streater, PCT, spin and statistics and all that
Bogolubov et al, Introduction to axiomatic quantum field theory
Schlingemann, From euclidean field theory to quantum field theory
Jorgensen and Olafsson, Osterwalder-Schrader axioms - Wightman Axioms
K. Osterwalder and R. Schrader, Axioms for Euclidean Green's functions, Commun Math Phys 31 (1973) 83--112.
Algebraic QFT
Fewster and Rejner, Algebraic Quantum Field Theory -- an introduction
Halvolson and Mueger, Algebraic Quantum Field Theory
Strocchi, An Introduction to Non-Perturbative Foundations of Quantum Field Theory
Haag, Local quantum physics
Araki, Mathematical theory of quantum fields
Brunetti et al, Advances in algebraic quantum field theory
Rejner, Perturbative Algebraic Quantum Field Theory
Baumgartel and Wollenberg, Causal nets of operator algebras
Baumgartel, Operator Algebraic Methods in Quantum Field Theory
Online: Local quantum physics crossroads
Constructive QFT
Introductory
A. Jaffe, Constructive quantum field theory
Abdesselam, QFT, RG, and all that, for mathematicians, in eleven pages, arXiv:1311.4897 [math.PR]
Summers, A Perspective on Constructive Quantum Field Theory, arXiv:1203.3991 [math-ph]
R. Gurau, J. Magnen, V. Rivasseau, Tree quantum field theory, Annales Henry Poincare 10 (2009) 867--891
J. Magnen, V. Rivasseau, Constructive ϕ 4 Field Theory without Tears, Annales Henri Poincare 9 (2008) 403--424
Glimm and Jaffe, Quantum Physics: a Functional Integral Point of View
Intermediate
Salmhofer: Renormalization: an introduction
V. F. Muller, Perturbative Renormalization by Flow Equations
D. C Brydges, Lectures on the renormalization group
A. Kupiainen, Introduction to the renormalization group
Fernandez, Frohlich and Sokal, Random Walks, Critical Phenomena and Triviality in Quantum Field Theory
Rivasseau, From Perturbative to Constructive Renormalization
Battle, Wavelets and Renormalization
Mastropietro, Non-Perturbative Renormalization
Benfatto and Gallavotti, Renomalization group
Feldman, Knorrer and Trubowitz, Fermionic Functional Integrals and the Renormalization Group
Costello, Renormalization and Effective Field Theory
Advanced
J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]
J. Dimock, "The Renormalization Group According to Balaban III. Convergence", arXiv:1304.0705 [math-ph]
J. Magnen, V. Rivasseu, R. Seneor, Construction of YM4 with an infrared cutoff, Commun. Math. Phys. 155(2): 325-383 (1993).
Glimm and Jaffe, Quantum Field Theory and Statistical Mechanics: Expositions
Glimm and Jaffe, Collected Papers: Constructive Quantum Field Theory
Relevant mathematics
- functional analysis, operator theory and PDEs
- distribution theory
- measure and probability theory
- representations of Lie groups and Lie algebras
- some combinatorics
- some representation theory of associative algebras.
Special subjects