Hamiltonian LGT in the complete Fourier analysis basis

Details Hamiltonian LGT in the complete Fourier analysis basis Hamiltonian LGT in the complete Fourier analysis basis

1999-09-09

arxiv.org/abs/hep-lat/9909067v1

Nucl.Phys.Proc.Suppl. 83 (2000) 926-928

Physics

High Energy Physics

High Energy Physics - Lattice

LATTICE99 (theoretical developments), 3 pages

Scientific paper

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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