Communications in Mathematical Physics

, Volume 267, Issue 1, pp 25–64 | Cite as

Quasi-Linear Quantum Field Theories for Maps to Groups and Their Quotients

  • Clifford H. TaubesEmail author


I describe a functional integral for maps from \(\mathbb{R}\times \mathbb{R}^{\rm n}\) to a Lie group or its quotient which has a simple renormalization that leads to a quantum field theory for maps from \(\mathbb{R}^{\rm n}\) into the Lie group or its quotient whose Hamiltonian is the time translation generator for a unitary action of the n+1 dimensional Poincaré group on the quantum Hilbert space. I also explain how the renormalization provides a functional integral for maps from a Riemann surface to a compact Lie group or its quotient that exhibits many conformal field theoretic properties.


Hilbert Space Riemann Surface Gaussian Measure Compact Riemann Surface Exterior Derivative 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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