Topological Quantum Field Theory
Atiyah's axioms, Chern–Simons theory, and quantum invariants.
Topological Quantum Field Theory. Atiyah’s axioms, Chern–Simons theory, and quantum invariants.
Foundations and canonical references
The standard treatments of topological quantum field theory approach the subject from complementary angles. Deligne, Quantum Fields and Strings: A Course for Mathematicians (1999) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of topological quantum field theory or connect it to neighbouring problems. Topological quantum field theory (Witten, 1988) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for topological quantum field theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
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- textbook · primary · 1999Quantum Fields and Strings: A Course for Mathematiciansdeligne-1999, etingof-1999, freed-1999, jeffrey-1999, kazhdan-1999, morgan-1999, morrison-1999, witten-1999
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