Functional Solution Scheme for Relativistic Strong Coupling Theor

Abstract

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.