相关论文: Ambiguities in Pauli-Villars regularization
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
The techniques of Pauli-Villars regularization and discrete light-cone quantization are combined to analyze Yukawa theory in a single-fermion truncation. A special form of the Lanczos algorithm is constructed for diagonalization of the…
Model complexity in amplitude analyses is often a priori under-constrained since the underlying theory permits a large number of possible amplitudes to contribute to most physical processes. The use of an overly complex model results in…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
Renormalization group equations in a two-valley system with valley-splitting and intervalley scattering are derived in the presence of spin-splitting induced by a parallel magnetic field. The relevant amplitudes in different regimes set by…
The renormalization procedure for the Yang-Mills theory in the gauge free of the Gribov ambiguity is constructed. It is shown that all the ultraviolet infinities may be removed by renormalization of the parameters entering the classical…
In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals,…
We present the renormalization functions of dimensionally regularized $\phi^3$ theory in six dimensions up to loop order six in the minimal subtraction scheme.
Integral operators of Abel type of order a > 0 arise naturally in a large spectrum of physical processes. Their inversion requires care since the resulting inverse problem is ill-posed. The purpose of this work is to devise and analyse a…
We study quantum corrections to the scalar potential in classically scale invariant theories, using a manifestly scale invariant regularization. To this purpose, the subtraction scale $\mu$ of the dimensional regularization is generated…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
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…
The prescription for the $\gamma_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
Exactification is the process of obtaining exact values of a function from its complete asymptotic expansion. Here Stirling's approximation for the logarithm of the gamma function or $\ln \Gamma(z)$ is derived completely whereby it is…
The $\ell_{1\text{-}2}$ regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. This…