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arXiv · hep-lat/9909067

Hamiltonian LGT in the complete Fourier analysis basis

G. Burgio·R. De Pietri·H. A. Morales-Tecotl·L. F. Urrutia·J. D. Vergara
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Abstract

The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We short-cut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Our analysis is based only on properties of the tensor category of Lie-Group representations. The Hamiltonian of such theories is calculated yielding a sparse matrix whose spectrum and eigenstates could be exactly derived as functions of the coupling $g^2$

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G. Burgio, R. De Pietri, H. A. Morales-Tecotl, L. F. Urrutia, J. D. Vergara. 1999-09-09. Hamiltonian LGT in the complete Fourier analysis basis. https://doi.org/10.1016/s0920-5632(00)91847-4

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