Related papers: Comparison of Improved Perturbative Methods
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…
The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…
We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge theory. We show that the conventional perturbative series for the partition function has a zero radius of convergence and is asymptotic. The average plaquette is…
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 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.…
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of…
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…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using…
Using the example of a two dimensional four-fermion lattice field theory we demonstrate that Feynman diagrams can generate a mass gap when massless fermions interact via a marginally relevant coupling. We introduce an infrared cutoff…
Perturbative techniques are important for modified theories of gravity since they allow to calculate deviations from General Relativity without recurring to exact solutions, which can be difficult to find. When applied to models such as…
We report MC calculations of perturbative coefficients for lattice scalar field theory in dimensions 1, 2 and 3, where the large field contributions are cutoff. This produces converging (instead of asymptotic) perturbative series. We…
The standard perturbation theory in QFT and lattice models leads to asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the…
A trial application of the method of Feynman-Kleinert approximants is made to perturbation series arising in connection with the lattice Schwinger model. In extrapolating the lattice strong-coupling series to the weak-coupling continuum…
The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field…
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…
A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their…