Related papers: A massless quantum field theory over the p-adics
Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor…
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
This manuscript (hep-th/9906140v1) is incomplete. Please read instead S. D. G{\l}azek, T. Mas{\l}owski, Renormalized Poincar\'e algebra for effective particles in quantum field theory, Phys.Rev. D65 (2002) 065011, (hep-th/0110185).
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
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 analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
These lecture notes introduce exact Wilsonian renormalisation, and describe its technical approach, from an intuitive implementation to more advanced realisations. The methods and concepts are explained with a scalar theory, and their…
This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts.…
Talk given at the conference "Visions in Mathematics toward the year 2000", August 1999, Tel-Aviv.
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
In this paper we present a new construction of analytic analogues of quantum groups over non-Archimedean fields and construct braided monoidal categories of their representations. We do this by constructing analytic Nichols algebras and use…
A redesigned starting point for covariant \phi^4_n, n\ge 4, models is suggested that takes the form of an alternative lattice action and which may have the virtue of leading to a nontrivial quantum field theory in the continuum limit. The…
We suggest a new mass generation mechanism for gauge fields. The quantum field theory constructed in this paper is nonabelian, gauge invariant and asymptotically free.
A hallmark of non-perturbative theories of quantum gravity is the absence of a fixed background geometry, and therefore the absence in a Planckian regime of any notion of length or scale that is defined a priori. This has potentially…
1. Introduction 2. Massless QCD and Scale Invariance 3. The Renormalisation Group and Asymptotic Freedom 4. More on the Running Coupling 5. Application to Hard Processes 5.1 $R_{e^+e^-}$ and Related Processes 5.2 The Final State in $e^+e^-$…
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…