New Method for Exact Calculation of Green Functions in Scalar Field Theory

概要

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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 costructed 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.
理論物理学刊行会の論文
1996-02-25