Method of loops applied to lattice gauge theory

The eigenvalue problem for the Hamiltonian of SU(2) lattice gauge theory is formulated in the loop representation, which is based on the fact that the physical Hilbert space can be spanned by states which are labeled by loops. Since the inner product between loop states can be calculated analytically, the eigenvalue problem is expressed in terms of vector components and matrix elements with respect to the loop basis. A small-scale numerical computation in 2+1 dimensions yields results which agree with results obtained from other methods.