相关论文: Ambiguities in Pauli-Villars regularization
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
We derive a divergence formula for a group of regularization methods with an L2 constraint. The formula is useful for regularization parameter selection, because it provides an unbiased estimate for the number of degrees of freedom. We…
The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the…
The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
It is established existence, uniqueness and multiplicity of solutions for a quasilinear elliptic problem problems driven by $\Phi$-Laplacian operator. Here we consider the reflexive and nonreflexive cases using an auxiliary problem. In…
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…
In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class…
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…
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…
I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
This paper serves as a first foray on regularisation for planar vector fields. Motivated by singularities in celestial mechanics, the block regularisation of a generic class of degenerate singularities is studied. The paper is concerned…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars…
We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus…