Related papers: Quantum corrections to Higher-Dimensional Theories
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
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…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. A dressed scheme for the perturbation expansion is proposed. It is proven that in this scheme a nonrenormalizable interaction becomes…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
We examine the QCD perturbation series at large orders, for different values of the 'large $\beta_0$ renormalization scale'. It is found that if we let this scale grow exponentially with the order, the divergent series can be turned into an…
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly…
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
We study how theories defined in (extra-dimensional) spaces with localized defects can be described perturbatively by effective field theories in which the width of the defects vanishes. These effective theories must incorporate a…
We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute…
Higher order renormalons beyond the chain of one-loop bubbles are discussed. A perturbation method for the infrared renormalon residue is found. The large order behavior of the current-current correlation function due to the first infrared…
The effects of quadratic order terms in the dispersion matrix near a mode conversion are considered. It is shown that including the corrections due to these quadratic terms gives a better matching between the local solution in the mode…
I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
A common approach in physics and mathematics is to extend and modify theories and frameworks by considering what is often described as a `natural' extension or modification by including higher-order terms or by introducing other…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.