This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of afgr;4 field theory is presented as a practical application.(For simplicity we restrict our analysis to the study of only vacuum-vacuum diagrams, the extension to the general case presents no difficulty). ... field and let us treat connected and disconnected diagrams on the same footing ( Translational invariance is completely destroyed). ... Let us consider the probability distribution uk(x1, x2, x3, x4) ofthe four vertices after the removal ofthe two lines (we neglect theanbsp;...
|Title||:||Large-Order Behaviour of Perturbation Theory|
|Author||:||J.C. Le Guillou, J. Zinn-Justin|
|Publisher||:||Elsevier - 2012-12-02|