## Abstract

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.

Original language | English |
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Pages (from-to) | 389-407 |

Number of pages | 19 |

Journal | Progress of Theoretical Physics |

Volume | 95 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1996 Feb |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)