Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-05-29
Phys.Rev. D57 (1998) 6429-6440
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, latex, 2 figures in ps format plus 2 figures included in the tex file. Uses epsf and psfig. New references appear
Scientific paper
10.1103/PhysRevD.57.6429
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in a form that can be minimized numerically. A scheme of successive refinements of the superposition is proposed that may converge to the exact functional. As an illustration, a simple numerical approximation for the effective potential is worked out based on minimization with respect to five variational parameters. A variational principle is formulated for the fermion vacuum energy as a functional of the scalar fields to which the fermions are coupled. The discussion in this paper is given for scalar and fermion interactions in 1+1 dimensions. The extension to higher dimensions encounters a more involved structure of ultraviolet divergences and is deferred to future work.
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