2005/10/25 by Manu Raj Mathur, Manu Mathur · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge boson #Gauge fixing #Gauge theory #Hamiltonian lattice gauge theory #Lattice (music) #Lattice field theory #Lattice gauge theory #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum electrodynamics #Quantum gauge theory #Quantum many-body systems #Theoretical physics #hep-lat #hep-th
paper · pdf · doi:10.1016/j.physletb.2006.08.022
published as Phys.Lett. B640 (2006) 292-296 · 4 pages, 2 figures, typos corrected
arxiv created 2005/10/25 · openalex publication_date 2006/08/25 · arxiv updated 2009/12/01 · openalex created_date 2017/05/26 · openalex updated_date 2026/08/05
We solve the Gauss law as well as the corresponding Mandelstam constraints of (d+1) dimensional SU(2) lattice gauge theory in terms of harmonic oscillator prepotentials. This enables us to explicitly construct a complete orthonormal and manifestly gauge invariant basis in the physical Hilbert space. Further, we show that this gauge invariant description represents networks of unoriented loops carrying certain non-negative abelian fluxes created by the harmonic oscillator prepotentials. The loop network is characterized by 3(d-1) gauge invariant integers at every lattice site which is the number of physical degrees of freedom. Time evolution involves local fluctuations of these loops. The loop Hamiltonian is derived. The generalization to SU(N) gauge group is discussed.