Related papers: Quantum Field Theory as a Problem of Resummation (…
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation…
Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
Given a Taylor series with a finite radius of convergence, its Borel transform defines an entire function. A theorem of P\'olya relates the large d istance behavior of the Borel transform in different directions to singularities of the…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
A new method of estimating higher order perturbative coefficients is discussed. It exploits the rapid, asymptotic growth of perturbative coefficients and the information on the singularities in the complex Borel plane. A comparison with…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested…
In quantum field theory the vacuum expectation values of physical observables, bilinear in the field operator, diverge. Among the most important points in the investigations of those expectation values is the regularization of divergent…
We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
In this paper we discuss how seemingly different notions of locality and causality in quantum field theory can be unified using a non-abelian generalization of the Hammerstein property (originally introduced as a weaker version of…
Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $\lambda \phi^4$ theory in two dimensions in the…