Talk presented by Giuseppe Burgio

Parallel Session: Theoretical Developments III

Friday July 2nd, 17.00 - 17.20, Room 8

The spectrum of Hamiltonian $LGT_q$ in the complete Fourier analysis basis

Abstract: The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis which avoids the over-completeness arising from the well known Mandelstam relations. We short-cut this problem using Harmonic analysis on Lie-Groups and the formalism of intertwining operators to explicitly construct a basis of the Hilbert space. Such construction is performed in a complete abstract way using only the properties of the tensor category of the representations of Lie-Groups. As a consequence, our analysis can be generalized to more abstract tensor category as the finite dimensional category of the quantum group $SU_q(N)$. The Hamiltonian of such theories can be very easily calculated, resulting in sparse matrix whose spectrum and eigenstates could in priciple be derived exactly as a function of the coupling $g^2$.

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