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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
Article
  • 82 Downloads

Abstract

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.

Keywords

Hilbert Space Riemann Surface Gaussian Measure Compact Riemann Surface Exterior Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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