MATRIX-ELEMENTS OF THIEMANN HAMILTONIAN CONSTRAINT IN LOOP QUANTUM-GRAVITY

We present an explicit computation of matrix elements of the Hamiltoni an constraint operator in non-perturbative quantum gravity. In particu lar, we consider the Euclidean term of Thiemann's version of the const raint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques fro m the recoupling theory of coloured knots and links. We exhibit the ma trix elements of the Hamiltonian constraint operator in the spin-netwo rk basis in compact algebraic form.