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.
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Communicated by A. Connes
Support in part by a grant from the National Science Foundation
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Taubes, C.H. Quasi-Linear Quantum Field Theories for Maps to Groups and Their Quotients. Commun. Math. Phys. 267, 25–64 (2006). https://doi.org/10.1007/s00220-006-0073-6
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DOI: https://doi.org/10.1007/s00220-006-0073-6