It has been argued by Dyson that the perturbation theory in coupling constant in QED can not be convergent. We provide similar arguments for the divergence of the series of 1 Nf expansion in QED. This result should hold for large class of QFTs where such an expansion is under taken. PACS numbers:03.65.-w,11.01.-z,12.20.-m

We make use of the path integral representation of the diffusion Green’s function to derive a renormalized perturbation expansion for the propagation of diffuse waves in an inhomogeneous medium. The first term in the expansion coincides with the Rytov approximation. The higher order terms can be used to develop a direct reconstruction method for time-resolved optical tomography.

Even for short-distance dominated observables the QCD perturbation expansion is never complete. The divergence of the expansion through infrared renormalons provides formal evidence of this fact. In this article we review how this apparent failure can be turned into a useful tool to investigate power corrections to hard processes in QCD.

For a class of multidimensional linear perturbation problems of considerable significance in applications, the Poincarc-Lighthill technique is shown to give first-order expansion terms which grow unbounded relative to the leading term (secular behavior), while the method of linear time scales leads to well-behaved expansion terms. A solvable example is introduced for comparison with the exact s...

In flat space-time, sigma-model strings and textures are both unstable to collapse and subsequent decay. With sufficient cosmological expansion, however, they are stable in a generalized sense: a small perturbation will cause them to change their shape, but they do not decay. The current rate of expansion is sufficient to stabilize strings, but not textures.

We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.

To study the convergence of the loop expansion at the high–temperature electroweak phase transition, we calculate the 2–loop effective potential of the 3d SU(2)–Higgs model in a general covariant gauge. We find that the loop expansion definitely breaks down for large ξ, but converges rather well for smaller values, deep in the broken phase. 1 Electronic address: [email protected] Recently...

When we calculate gravitational waveforms from extreme-mass-ratio inspirals by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate the linear metric perturbation induced by geodesics orbiting a black hole, then we calculate the adiabatic evolution of the parameters of geodesics due to the radiation reaction effect through...

The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one di...

Perturbation theory is the standard method to study quantum field theories in the small coupling regime. However, the interplay of the perturbative expansion and the thermodynamic limit remains controversial. In particular, arguments were put forward that the infinite volume limit of perturbative coefficients does not give the correct infinite volume asymptotic perturbation expansion of asympto...