相关论文: Implicit Regularisation Technique: Calculation of …
We have developed an efficient algorithm for the subtraction of infrared divergences that arise in the evaluation of QED corrections to the anomalous magnetic moment of lepton (g-2). By incorporating this new algorithm, we have extended the…
Using the higher covariant derivatives regularization of gauge theories in the framework of the background field method, supplemented with one-loop Pauli-Villars regulator fields, we obtain a version of the renormalization group equation…
We compute the two-loop QCD helicity amplitudes for the process e^+e^- --> q bar{q} g. The amplitudes are extracted in a scheme-independent manner from the coefficients appearing in the general tensorial structure for this process. The…
In this note we study worldsheet two- and four-point functions at the one-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first address the regularization ambiguity that appears in the dispersion relation derived from…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
This article introduces new multiplicative updates for nonnegative matrix factorization with the $\beta$-divergence and sparse regularization of one of the two factors (say, the activation matrix). It is well known that the norm of the…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…
We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for…
In the paper, we study the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for the contribution in terms of three functions, formed from the Green's function expansion…
Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…
In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $\beta$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of…
The high-energy factorization of gauge theory scattering amplitudes in terms of universal impact factors and a Reggeized exchange in the $t$-channel, corresponding to a Regge pole in the angular momentum plane, is know to conflict with the…
The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales,…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
We study the three-loop gauge $\beta$-functions in general $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of…
Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous…
For the anisotropic $[u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]$-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic…
We calculate the finite temperature effective potential of $\lambda\phi^4$ at the two loop order of the 2PPI expansion. This expansion contains all diagrams which remain connected when two lines meeting at the same point are cut and…
We study the $\frac{\lambda}{4!}\phi^{4}$ massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking…