Related papers: On the Connection Between Momentum Cutoff and Oper…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
The problem of UV divergences in QFT has long been a fundamental challenge. Standard regularization techniques modify high-energy behavior to ensure well-defined integrals. However, these approaches often introduce unphysical parameters,…
Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin 1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate…
We address here the topological equivalence of knots through the so-called Reidemeister moves. These topology-conserving manipulations are recast into dynamical rules on the crossings of knot diagrams. This is presented in terms of a simple…
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…
Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop…
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…
We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show…
We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
The paper is devoted to the three-loop renormalization of the effective action for a two-dimensional non-linear sigma model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of…
Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed…
We construct a gauge invariant regularisation scheme for pure SU(N) Yang-Mills theory in fixed dimension four or less (for N = infinity in all dimensions), with a physical cutoff scale Lambda, by using covariant higher derivatives and…
The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${\bf x}={\bf x}(\tau)$, $t=t(\tau)$ instead of ${\bf x}={\bf…