Related papers: A topological approach to renormalization and its …
Using six-dimensional quantum electrodynamics ($QED_6$) as an example we study the one-loop renormalization of the theory both from the six and four-dimensional points of view. Our main conclusion is that the properly renormalized four…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Geometric engineering is a collection of tools developed to establish dictionaries between local singularities in string theory and (supersymmetric) quantum fields. Extended operators and defects, as well as their higher quantum numbers…
By combining two distinct renormalization group transformations, opposing scale transformations, we obtain a composite transformation which does not rescale the system, and drives it to a "geometrical" fixed point, controlling the effective…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
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…
The Wilsonian renormalization group implies that an arbitrary four dimensional field theory with an ultraviolet cutoff is equivalent to a theory which is renormalizable by power counting at energy scales much below the cutoff. This applies…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
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.…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale $\L_R > 0$. We…
We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping…
We consider renormalizability of topologically massive gravity in three space-time dimensions. With a usual parametrization of the metric tensor, we establish the statement that topologically massive gravity is in fact renormalizable. In…
A new topological model is proposed in three dimensions as an extension of the BF-model. It is a three-dimensional counterpart of the two-dimensional model introduced by Chamseddine and Wyler ten years ago. The BFK-model, as we shall call…
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…
We showed in part I (hep-th/9912092) that the Hopf algebra ${\cal H}$ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group $G$ and that the renormalized theory is obtained from the…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
We study the dynamics of the renormalization operator acting on the space of pairs (v,t), where v is a diffeomorphism and t belongs to [0,1], interpreted as unimodal maps x-->v(q_t(x)), where q_t(x)=-2t|x|^a+2t-1. We prove the so called…
Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…