Related papers: Positivity and Convergence in Fermionic Quantum Fi…
We give an indication that gravity coupled to an infinite number of fields might be a renormalizable theory. A toy model with an infinite number of interacting fermions in four-dimentional space-time is analyzed. The model is finite at any…
This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose…
It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS…
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…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We show that the direction of renormalization in effective field theory is constrained by fundamental principles in the infrared$\unicode{x2014}$unitarity, analyticity, and Lorentz invariance. Our theorem, in the spirit of the $a$-theorem…
Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original "microscopic" theory of interacting fermions based on the spectral decomposition…
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis…
We consider eventually positive operator semigroups and study the question whether their eventual positivity is preserved by bounded perturbations of the generator or not. We demonstrate that eventual positivity is not stable with respect…
We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion,…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…
The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background…
We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an…
I provide a straightforward proof that a simple harmonic oscillator perturbed by an (almost) arbitrary positive interaction has a perturbative expansion for any finite-time Euclidian transition amplitude which obeys the following result:…
Positivity bounds on scattering amplitudes provide a necessary condition for a low-energy effective field theory to have a consistent ultraviolet completion. Their extension to gravity theories has been studied in the past years aiming at…
The problem of understanding the role of large gauge transformations in thermal field theories has recently inspired a number of studies of a one dimensional field theory. Such work has led to the conclusion that gauge invariance is…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric.…