1995/04/30 by Damiano Anselmi · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Embedding #Field (mathematics) #Instanton #Mathematical physics #Mathematics #Moduli space #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Theoretical physics #Topological quantum field theory #Topological quantum number #Topology (electrical circuits) #hep-th
paper · pdf · doi:10.1088/0264-9381/14/1/005
published as Class.Quant.Grav. 14 (1997) 1-20 · 23 pages, 1 figure. Revision: additional explanations
arxiv created 1995/11/21 · openalex publication_date 1997/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Topological Yang - Mills theory with the Belavin - Polyakov - Schwarz - Tyupkin SU(2) instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discussed. By embedding topological Yang - Mills theory into pure Yang - Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors. In particular, TQFT classifies the set of good measures over the instanton moduli space and solves the inconsistency problems of the previous approaches. The qualitatively new physical implications are pointed out. Link numbers in QCD are related to a non-Abelian analogue of the Aharonov - Bohm effect.