Related papers: Regularization, Renormalization, and Dimensional A…
Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent…
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 show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves…
We suggest a non-minimal renormalization scheme based on dimensional regularization that naturally incorporates threshold effects of heavy particles. By renormalizing couplings and masses to subtract all poles in $d \geq 4$, the resulting…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer 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…
A divergence-free approach to relativistic quantum electrodynamics based on regularisation of equations of quantum mechanics is discussed. This approach is shown to be exactly equivalent to the conventional Feynman-Dyson renormalisation…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
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…
We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N=1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG…
We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…
The controversy concerning the phenomenon of breakdown of dimensional regularization in the problems involving asymptotic expansions of Feynman diagrams in non-Euclidean regimes is discussed with some pertinent bibliographic comments.
One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…