Explicit Functional Integration Method for Determining Approximate Stationary States in Quantum Field Theories
The Ray1eigh-Ritz procedure for functionalities, an explicit functional integration method for determining approximate stationary states in quantum field theories, is described and illustrated here for certain models with simply chosen expressions for the trial state functionals. Approximate vacuum, one-particle and two-particle (noninteracting, bound or scattering) stationary states are derived for generic self-interacting real scalar theories without renormalization, for a nonre1ativistic real scalar-Weyl spinor model with renormalization, and for a self — interacting complex scalar model with renormalization.
KeywordsFunctional Integration Hamiltonian Operator Energy Functionality Relativistic Wave Equation Real Scalar Field
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- 1.See, for example, J.P. Hsu, Phys.Rev.Letters 36, 646 (1976); M.Creutz, “Quantum Mechanics of Extended Objects in Relativistic Field Theory” (preprint of paper to appear in Physical Review D); J.Hietarinta, “On the Existence of Confied Solutions in Nonlinear Chiral Theories” (preprint of paper to appear in Physical Review D), and works cited therein. Alternative functional integration and other approaches to quantized “particlelike” solutions have been proposed by other authors, including :ADSCrossRefGoogle Scholar