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arXiv · hep-th/9705230

Variational Wave Functionals in Quantum Field Theory

George Tiktopoulos
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Abstract

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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George Tiktopoulos. 1997-06-20. Variational Wave Functionals in Quantum Field Theory. https://doi.org/10.1103/physrevd.57.6429

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