'Variational' optimization in quantum field theory

[摘要] 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 $lambdaphisp4$ theory we discuss variational calculations of the effective potential that go beyond the Gaussian approximation. Trial wavefunctionals are constructed by applying a unitary operator $U = esp{-ispisb{R}phisbsp{T}{2}}$ to a Gaussian state. We calculate the expectation value of the Hamiltonian using the non-Gaussian trial states generated, and thus obtain optimization equations for the variational-parameter functions of the ansatz. At the origin, $varphisb{c} = 0,$ 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 third-order quantum chromodynamics (QCD) corrections to $Rsb{esp+esp-}.$ 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 Poggio-Quinn-Weinberg 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 $alphasb{s}/pi = 0.26,$ which is in remarkable concordance with values obtained phenomenologically.

[发布机构] Rice University

[效力级别] particles