PATH-INTEGRAL LOOP REPRESENTATION OF 2-LATTICE NON-ABELIAN GAUGE-THEORIES - ART. NO. 045007(1)

A gauge invariant Hamiltonian representation for SU(2) in terms of a s pin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The corresponding path integral for SU(2) latt ice gauge theory is expressed as a sum over colored surfaces, i.e. onl y involving the j(p) attached to the lattice plaquettes. These surface s may be interpreted as the world sheets of the spin networks in 2+1 d imensions; this can be accomplished by working in a lattice dual to a tetrahedral lattice constructed on a face centered cubic Bravais latti ce. On such a lattice, the integral of gauge variables over boundaries or singular lines - which now always bound three colored surfaces - o nly contributes when four singular lines intersect at one vertex and c an be explicitly computed producing a 6-j or Racah symbol. We performe d a strong coupling expansion for the free energy. The convergence of the series expansions is quite different from the series expansions wh ich were performed in ordinary cubic lattices. Our series seems to be more consistent with the expected linear behavior in the weak coupling limit. Finally, we discuss the connection in the naive continuum limi t between this action and that of the B-F topological field theory and also with the pure gravity action. [S0556-2821(98)05914-1].