Related papers: Resummation and renormalons in a general Quantum F…
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…
The renormalon singularities are a known source of the divergent behavior of asymptotic perturbative series from field theoretical models. These singularities live in the Borel plane and are responsible for ambiguities in the physical…
We introduce the concept of a holomorphic field theory on any complex manifold in the language of the Batalin-Vilkovisky formalism. When the complex dimension is one, this setting agrees with that of chiral conformal field theory. Our main…
We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas, and great…
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
Nonrenormalizable quantum field theories require counterterms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counterterms suggested by renormalized perturbation…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
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…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…
We shortly illustrate how the field-theoretic approach to critical phenomena takes place in the more complete Wilson theory of renormalization and qualitatively discuss its domain of validity. By the way, we suggest that the differential…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
The possibility is discussed that existence of renormalon singularities is not the internal property of the specific field theory but depends on the renormalization scheme.
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based…
We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the…
Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to…