Loop approach to lattice gauge theories Original Research Article

We solve the Gauss law and the corresponding Mandelstam constraints in the loop Hilbert space image using the prepotential formulation of image-dimensional image lattice gauge theory. The resulting orthonormal and complete loop basis, explicitly constructed in terms of the image prepotential intertwining operators, is used to transcribe the gauge dynamics directly in image without any redundant gauge and loop degrees of freedom. Using generalized Wigner–Eckart theorem and Biedenharn–Elliot identity in image, we show that the above loop dynamics for pure SU(2) lattice gauge theory in arbitrary dimension, is given by real and symmetric image coefficients of the second kind (e.g., image, 10 for image, 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.