相关论文: New Optimization Methods for Converging Perturbati…
For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical…
For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that…
For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that…
We show that for two non-trivial lambda phi ^4 problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative series can be obtained by cutting off the large field contributions. The modified series…
The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For $\lambda \phi^4$ models, the perturbative series have a zero radius of convergence which in part motivated the design of…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
The perturbation series for the renormalization group functions of the $O(N)-$symmetric $\phi^4$ field theory are divergent but asymptotic. They are usually followed by Resummation calculations to extract reliable results. Although the same…
We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected.…
We apply the linear $\delta$-expansion (LDE), originally developed as a nonperturbative, analytical approximation scheme in quantum field theory, to problems involving noninteracting electrons in disordered solids. The initial idea that the…
Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional…
The thermodynamics of a scalar field with a quartic interaction is studied within the linear delta expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…
In pure gauge SU(3) near beta = 6, weak and strong coupling expansions break down and the MC method seems to be the only practical alternative. We discuss the possibility of using a modified version of perturbation theory which relies on a…
Physical quantities in QCD are independent of renormalization scheme (RS), but that exact invariance is spoiled by truncations of the perturbation series. "Optimization" corresponds to making the perturbative approximant, at any given…
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by…