Loop Approach to Lattice Gauge Theories
| dc.creator | Mathur, Manu | |
| dc.date | 2007-02-03 | |
| dc.date | 2007-05-07 | |
| dc.date.accessioned | 2026-07-07T11:22:04Z | |
| dc.date.available | 2026-07-07T11:22:04Z | |
| dc.description | We solve the Gauss law and the corresponding Mandelstam constraints in the loop Hilbert space ${\cal H}^{L}$ 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 ${\cal H}^{L}$ without any redundant gauge and loop degrees of freedom. Using generalized Wigner-Eckart theorem and Biedenharn -Elliot identity in ${\cal H}^L$, 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. | |
| dc.description | 32 pages, 9 figures, typos corrected, new references added (to be published in Nucl. Phys. B) | |
| dc.identifier | https://arxiv.org/abs/hep-lat/0702007 | |
| dc.identifier | http://arxiv.org/abs/hep-lat/0702007 | |
| dc.identifier | Nucl.Phys.B779:32-62,2007 | |
| dc.identifier | doi:10.1016/j.nuclphysb.2007.04.031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/194449 | |
| dc.subject | High Energy Physics - Lattice | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Loop Approach to Lattice Gauge Theories | |
| dc.type | text |