2007/02/28 by Manu Raj Mathur, Manu Mathur · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.04.031
published as Nucl.Phys.B779:32-62,2007 · 32 pages, 9 figures, typos corrected, new references added (to be published in Nucl. Phys. B)
openalex publication_date 2007/05/06 · arxiv created 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve the Gauss law and the corresponding Mandelstam constraints in the loop Hilbert space \cal HL using the prepotential formulation of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete loop basis, explicitly constructed in terms of the d(2d-1) prepotential intertwining operators, is used to transcribe the gauge dynamics directly in \cal HL without any redundant gauge and loop degrees of freedom. Using generalized Wigner-Eckart theorem and Biedenharn -Elliot identity in \cal HL, we show that the loop dynamics for pure SU(2) lattice gauge theory in arbitrary dimension, is given by the real symmetric 3nj symbols of first kind (e.g., n=6, 10 for d=2, 3 respectively). The corresponding "ribbon diagrams" representing SU(2) loop dynamics are constructed. The prepotential techniques are trivially extended to include fundamental matter fields leading to a description in terms of loops and strings. The SU(N) gauge group is briefly discussed.