Related papers: Equivalence of Dimensional Reduction and Dimension…
While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that…
We propose a dimensional regularization scheme in the light-cone gauge NSR superstring field theory to regularize the divergences caused by the colliding supercurrents inserted at the interaction points. We study the tree amplitudes and…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
Effective regularisation during training can mean the difference between success and failure for deep neural networks. Recently, dither has been suggested as alternative to dropout for regularisation during batch-averaged stochastic…
Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…
We outline the evaluation of $n$-dimensional fermion traces ($n\in\mathbb{N}$) built by products of Dirac-$\gamma$ matrices suitable for a uniform dimensional continuation. Such a continuation is needed for calculations employing a…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
We investigate the issue of regularization/renormalization in the presence of a nontrivial background in the case of 1+1-(supersymmetric) solitons. In particular we study and compare the commonly employed regularization methods (mode-…
We consider procedures through which an ultraviolet cut-off regularization scheme can be modified to reproduce the same results for nonperturbative renormalized Green's functions as obtained from a dimensional regularization scheme. These…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
We calculate symmetry-restoring counterterms in supersymmetric QCD at the one-loop level. First we determine loop corrections to the supersymmetry and gauge transformations and find counterterms in such a way that the symmetry algebra holds…
It is known that factorization of the $\beta$-function loop integrals into integrals of double total derivatives is an important ingredient needed for deriving the NSVZ relation by direct perturbative calculations in ${\cal N}=1$ SQED…
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 introduce DFReg, a physics-inspired regularization method for deep neural networks that operates on the global distribution of weights. Drawing from Density Functional Theory (DFT), DFReg applies a functional penalty to encourage smooth,…
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 explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $\beta$-function, we derive the transformation of $\alpha^{\DRED}$ to $\alpha^{\NSVZ}$ through terms of order $\alpha^4$. We…
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…