We present a new method for calculating the Green functions for a lattice scalar field theory in D dimensions with arbitrary potential V(φ). The method for non-perturbative evaluation of Green functions for D = 1 is generalized to higher dimensions. We define "hole functions" A(i) (i=0, 1, 2, ⋯, N-1) from which one can construct N-point Green functions. We derive characteristic equations of A(i) that form a finite closed set of coupled local equations. It is shown that the Green functions constructed from the solutions to the characteristic equations satisfy the Dyson-Schwinger equations. To fix the boundary conditions of A(i), a prescription is given for selecting the vacuum state at the boundaries.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)