Related papers: Four-dimensional regularization of higher-order co…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
Four-dimensional renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet (UV) counterterms.…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
We show that, by viewing a 4D effective-field theory as the infrared (IR) limit of the compactified version in 5D, we can compute two-loop anomalous dimensions without gauge-breaking counter-terms, IR re-arrangement or geometric methods.…
We calculate field theory loop amplitudes by string methods, applied to half-maximal 4-point one-loop graviton amplitudes. Infrared divergences are regulated similarly to soft-collinear effective field theory (SCET): new mass scales are…
We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
Without using conformal transformation, a simple type of five-dimensional $f(R)-$brane model is linearized directly in its higher-order frame. In this paper, the linearization is conducted in the equation of motion approach. We first derive…
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on dropping/penalizing weights in a global…
We review the Four-Dimensional-Formulation variant of the Four-Dimensional-Helicity scheme, by showing two applications of this regularisation scheme. The first one is the computation of one-loop helicity amplitudes, for which we present…
We present an extension of the renormalisation procedure based on the R-operation in $D$ dimensions at two-loop level, in which the numerators of all Feynman diagrams can be constructed in four dimensions, and the rational terms stemming…
We propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…