'variational' Optimization in Quantum Field Theory
Abstract
We examine two different techniques for studying quantum field theories in which a 'variational' optimization of parameters plays a crucial role. In the context of the O(N)symmetric lambdaphi^4 theory we discuss variational calculations of the effective potential that go beyond the Gaussian approximation. Trial wavefunctionals are constructed by applying a unitary operator U = e^{ispi_{R}phi _sp{T}{2}} to a Gaussian state. We calculate the expectation value of the Hamiltonian using the nonGaussian trial states generated, and thus obtain optimization equations for the variational parameter functions of the ansatz. At the origin, varphi_{c} = 0, these equations can be solved explicitly and lead to a nontrivial correction to the mass renormalization, with respect to the Gaussian case. Numerical results are obtained for the (0 + 1)dimensional case and show a worthwhile quantitative improvement over the Gaussian approximation. We also discuss the use of optimized perturbation theory (OPT) as applied to the thirdorder quantum chromodynamics (QCD) corrections to R_{e^+e ^}. The OPT method, based on the principle of minimal sensitivity, finds an effective coupling constant that remains finite down to zero energy. This allows us to apply the PoggioQuinnWeinberg smearing method down to energies below 1 GeV, where we find good agreement between theory and experiment. The couplant freezes to a zero energy value of alpha_{s}/ pi = 0.26, which is in remarkable concordance with values obtained phenomenologically.
 Publication:

Ph.D. Thesis
 Pub Date:
 1993
 Bibcode:
 1993PhDT.......205M
 Keywords:

 QCD;
 Physics: General; Physics: Elementary Particles and High Energy