Related papers: $\gamma_5$ in Dimensional Regularization: a Novel …
We discuss the consistency of a new \gf -scheme with renormalization. In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. As a side effect we obtain a short proof of the Adler-Bardeen theorem.…
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…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
We develop a gauge-invariant formalism to describe metric perturbations in five-dimensional brane-world theories. In particular, this formalism applies to models originating from heterotic M-theory. We introduce a generalized longitudinal…
It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and…
The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model.…
We analyze a new approach to Machine Learning coming from a modification of classical regularization networks by casting the process in the time dimension, leading to a sort of collapse of dimensionality in the problem of learning the model…
Using the language of differential forms, the Kaluza-Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without…
An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
$\gamma_5$ 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…
General issues concerning the regularization of supersymmetric theories using dimensional regularization and dimensional reduction are reviewed. Recent progress on problems of dimensional reduction related to factorization, supersymmetry,…
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…
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'')…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
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 propose a gamma5 scheme in dimensional regularization by analytically continuing the dimension after all the gamma5 matrices have been moved to the rightmost position. All Feynman amplitudes corresponding to diagrams with no fermion…