Related papers: Dimensional regularization vs methods in fixed dim…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
A new Dimensional Regularization of $\gamma_5$ is proposed. Cyclicity and Lorentz covariance are enforced. The extension to generic dimension is based on the integral representation of the trace of gamma's, presented in a previous paper.
A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the…
A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms…
We examine the subtleties of regularization schemes in four-dimensional space ($4S$), related in particular to the introduction of the $\gamma_5$ matrix. To illustrate we use a "Bumblebee" model featuring dynamically induced Lorentz…
An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…
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 describe the equivalence at one loop between constrained differential renormalization and regularization by dimensional reduction in the MS scheme. To illustrate it, we reexamine the calculation of supergravity corrections to (g-2)_l.
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of gamma5. Also loop calculations in supersymmetric theories need a consistent definition of gamma5. In…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
$\gamma_5$ is notoriously difficult to define in $D$ dimensions. The traditional BMHV scheme employs a non-anticommuting $\gamma_5$. Its key advantage is mathematical consistency and the existence of all-order proofs. Its disadvantage is…
For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
We study a five dimensional Horava-Lifshitz like scalar QED with dynamical exponent z=2. Consistency of the renormalization procedure requires the presence of four quartic and one six-fold scalar couplings besides the terms bilinear in the…
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit…