Related papers: Numbers and Functions in Quantum Field Theory
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying…
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…
Recently, a new type of renormalizable $\phi^{\star 4}_{4}$ scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a $a/(\theta^2p^2)$ term. We calculate here…
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…
Leading logarithms (LLs) in massless non-renormalizable effective field theories (EFTs) can be computed with the help of non-linear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity,…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
I discuss the role of quantum effects in the phenomenology of effective supergravity theories from compactification of the weakly coupled heterotic string. An accurate incorporation of these effects requires a regularization procedure that…
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and…
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
In this paper, I show a close connection between renormalization and a generalization of the Dynkin operator in terms of logarithmic derivations. The geometric $\beta$ function, which describes the dependence of a Quantum Field Theory on an…
In this paper, we show how the finite formulation of QFT based on Callan-Symanzik equations can be generalised to the case of non-renormalizable theories. We derive an equation for effective action for an arbitrary single scalar field…
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.
By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in…
We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.
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…