The configuration space of gauge theory on open manifolds of bounded geometry

Jürgen Eichhorn; Gerd Heber

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Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez (2004)

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This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject. In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered...

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

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Let L(z) be the Lie norm on $\tilde{} = ℂ^{n + 1}$ and L*(z) the dual Lie norm. We denote by $_{Δ} (\tilde{B} (R))$ the space of complex harmonic functions on the open Lie ball $\tilde{B} (R)$ and by $E x p_{Δ} (\tilde{}; (A, L *))$ the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

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