A non-perturbative contribution to the vacuum energy in supersymmetric Yang-Mills theory

It is shown that the quantum fluctuations around an interacting instanton-anti-instanton field configuration induce negative vacuum energy in supersymmetric Yang-Mills theory.     

A non-perturbative approach to hyperfine splitting

A hyperfine energy splitting for atomic hydrogen is calculated in a non-perturbative manner for a finite width contact interaction. A close agreement between this result and first order perturbation theory is obtained.     

A non-perturbative approach to the bound polaron

An iterative method, applied to the bound polaron hamiltonian, reduces it in successive steps. Lowest order results, valid for all types of bindings, are obtained and compared with available pertubation results.     

A Dirac algebraic approach to supersymmetry

The power of the Dirac algebra is illustrated through the Kähler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5, 1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields.     

A superloop approach to supersymmetric gauge theories

A supersymmetric extension of the loop equations of motion in gauge theories is presented. The ansatz used for solving these superloop equations has the form of an average of the superloop product — supersymmetric path-dependent phase factor. The averaging action is determined by the superloop equations themselves. An example of the abelian spinor gauge superfield is considered in some detail.     

Electromagnetic mixing laws: A supersymmetric approach

In this article we address the old problem of finding the effective dielectric constant of materials described either by a local random dielectric constant, or by a set of non-overlapping spherical inclusions randomly dispersed in a host. We use a unified theoretical framework, such that all the most important Electromagnetic Mixing Laws (EML) can be recovered as the first iterative step of a family of results, thus opening the way to future improvements through the refinements of the approximation schemes. When the material is described by a set of immersed inclusions characterized by their spatial correlation functions, we exhibit an EML which, being featured by a minimal approximation scheme, does not come from the multiple scattering paradigm. It is made of a pure Hori-Yonezawa formula, corrected by a power series of the inclusion density. The coefficients of the latter, which are given as sums of standard diagrams, are recast into electromagnetic quantities which calculation is amenable numerically thanks to codes available on the web. The methods used and developed in this work are generic and can be used in a large variety of areas ranging from mechanics to thermodynamics.     

A non-perturbative approach to the infrared problem in QED: Construction of charged states

A non-perturbative treatment of the infrared problem in quantum electrodynamics is presented. Starting from the local and covariant correlation functions of the Gupta-Bleuler formulation an explicit construction of the physical charged states is given. They are shown to satisfy a non-(Lorentz) covariant infrared condition, of Bloch-Nordsieck type, compatible with the Gupta-Bleuler condition (resolution of Zwanziger's paradox). The breaking of the Lorentz group in the charged sectors and its physical meaning is explained. The infrared structure of the S-matrix elements between physical charged states is shown to be that of the classical Bloch-Nordsieck factors, (proof of the Bloch-Nordsieck ansatz), and to be simply related to that calculated by using local covariant states.     

A new method to solve the non-perturbative renormalization group equations

We propose a method to solve the non-perturbative renormalization group equations for the n-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the n-point functions. This is achieved: (i) by exploiting the decoupling of modes and the analyticity of the n  -point functions at small momenta: this allows us to neglect some momentum dependence of the vertices entering the flow equations; (ii) by relating vertices at zero momenta to derivatives of lower order vertices with respect to a constant background field. Although the approximation is not controlled by a small parameter, its accuracy can be systematically improved. When it is applied to the O(N)$O(N)$ model, its leading order is exact in the large-N limit; in this case, one recovers known results in a simple and direct way, i.e., without introducing an auxiliary field.     

Low-energy properties of non-perturbative quantum systems: A space reduction approach

We propose and test a renormalization procedure which acts in Hilbert space. We test its efficiency on strongly correlated quantum spin systems by working out and analyzing the low-energy spectral properties of frustrated quantum spin systems in different parts of the phase diagram and in the neighbourhood of quantum critical points.     

Interaction of electromagnetic field with the OH radical: A non-perturbative approach

A non-perturbative approach for the study of the interaction of a hydroxyl (OH) radical with infra-red radiation is presented. The dressed states and vibrational transition probability of OH radical are defined by a quasi-energy approach (non-perturbative).     

Stochastic processes and the non-perturbative structure of the QCD vacuum

Based on a local Gaussian evaluation of the functional integral representation, a method is developed to obtain ground state functionals. The method is applied to the gluon sector of QCD. For the leading term in the ground state functional, stochastic techniques are used to check consistency of the quantum theory, finiteness of the mass gap and the scaling relation in the continuum limit. The functional also implies strong chromomagnetic fluctuations which constrain the propagators in the fermion sector.     

A lagrangian formulation of the Wess approach to supersymmetric Yang-Mills theories

We obtain a superspace lagrangian density which reproduces the Wess formulation of supersymmetric gauge theories. The present approach, which is a first-order formalism, gives rise to a lagrangian density polynomial in the Yang-Mills and auxiliary superfields and appears to be stable under quantization and renormalization.     

A new perturbative approximation applied to supersymmetric quantum field theory

We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0.     

A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000