Related papers: Non-Commutative Renormalization
This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…
We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of…
We give a unified geometric approach to some theorems about primitive elements and palindromes in free groups of rank 2. The geometric treatment gives new proofs of the theorems. Dedicated to Bill Harvey on his 65th birthday.
Recently new methods have been introduced to investigate the non-renormalization properties of the anomalies at a non perturbative level and in presence of a lattice. The issue is relevant in a number of problems ranging from the…
We present a definition of and discuss basic properties of cross-ratios over noncommutative skew-fields. A new theorem was added.
As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of…
Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…
A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…
The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that,…
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of $T$-matrices are unraveled using rigorous solutions and an inverse form of algebraic Lippmann-schwinger equation. The intrinsic…
In many domains of physics, methods are needed to deal with non-perturbative aspects. I want here to argue that a good approach is to work on the Borel transforms of the quantities of interest, the singularities of which give…
We discuss the status and the problems related to the application of the off-shell non-perturbative renormalization method in a fixed gauge to operators relevant to weak decays. In particular, we critically reappraise the method recently…
This paper summarizes the contents of the paper "Non-Commutative Worlds" by the author (published in New Journal of Physics Vol. 6, November 2004, pp. 2 - 46; quant-ph/0403012) and gives a new derivation of our generalization of…
A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After…
We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order…
In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed…
We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from…
We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed in which a subtraction velocity nu is used rather than a subtraction scale mu. We derive…
This review was given at the 65th birthday meeting of D.W. Sciama, The Renaissance of General Relativity and Cosmology, to be published by Cambridge University Press. It presents progress in the understanding of non-standard relativistic…
We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we find divergent one-loop contributions to the 1-point and 2-point Green functions. We obtain that five counterterms are necessary for renormalization and that all…