TY - JOUR

T1 - New method for exact calculation of green functions in scalar field theory

AU - Sumino, Yukinari

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1996/2

Y1 - 1996/2

N2 - 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.

AB - 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.

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U2 - 10.1143/PTP.95.389

DO - 10.1143/PTP.95.389

M3 - Article

AN - SCOPUS:0030530789

VL - 95

SP - 389

EP - 407

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 2

ER -