Localization and diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories

DOI10.1063/1.531038zbMath0844.58105arXivhep-th/9501075OpenAlexW2015140685MaRDI QIDQ4871957

Matthias Blau, George Thompson

Publication date: 8 April 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9501075

zbMATH Keywords

topological field theorypath integralsgauge theoryfunctional integrals

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of global analysis to the sciences (58Z05) Path integrals in quantum mechanics (81S40) Supersymmetry and quantum mechanics (81Q60)

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Cites Work

• The Mathai-Quillen formalism and topological field theory
• Polynomial invariants for smooth four-manifolds
• The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
• Quantum Yang-Mills on a Riemann surface
• Zeros d'un champ de vecteurs et classes characteristiques équivariantes
• The moment map and equivariant cohomology
• Superconnections, Thom classes, and equivariant differential forms
• Localization formulas, superconnections, and the index theorem for families
• Cohomology of symplectomorphism groups and critical values of Hamiltonians
• Topological quantum field theory
• Canonical partition function of Hamiltonian systems and the stationary phase formula
• Topological sigma models
• On the variation in the cohomology of the symplectic form of the reduced phase space
• On quantum gauge theories in two dimensions
• Heat kernels and Thom forms
• Two dimensional gauge theories revisited
• Topological field theory and rational curves
• A strong coupling test of \(S\)-duality
• Monopoles, duality and chiral symmetry breaking in \(N=2\) supersymmetric QCD
• BRST model for equivariant cohomology and representatives for the equivariant Thom class
• \(N=2\) topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant
• Topological gauge theories of antisymmetric tensor fields
• Equivariant Bott-Chern currents and the Ray-Singer analytic torsion
• Derivation of the Verlinde formula from Chern-Simons theory and the \(G/G\) model.
• Phase space isometries and equivariant localization of path integrals in two dimensions
• Topological Lagrangians and cohomology
• ON QUANTUM INTEGRABILITY AND THE LEFSCHETZ NUMBER
• LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS
• The propagator for quantum mechanics on a group manifold from an infinite-dimensional analogue of the Duistermaat-Heckman integration formula
• GEOMETRY AND QUANTIZATION OF TOPOLOGICAL GAUGE THEORIES
• CHERN-SIMONS QUANTUM MECHANICS, SUPERSYMMETRY, AND SYMPLECTIC INVARIANTS
• TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS
• Symplectic manifolds, coherent states, and semiclassical approximation
• Supersymmetric Yang–Mills theory on a four-manifold
• Supersymmetry and the Atiyah-Singer index theorem

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