Related papers: The Background-Field Method and Noninvariant Renor…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We apply a novel background independent regularization scheme, the $N$-cutoffs, to self-consistently quantize scalar and metric fluctuations on the maximally symmetric but non-compact hyperbolic space. For quantum matter fields on a…
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…
Deviations from scale invariance resulting from small perturbations of a general two dimensional conformal field theory are studied. They are expressed in terms of beta functions for renormalization of general couplings under local change…
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…
Application of the background-field method to QCD and the electroweak Standard Model yields gauge-invariant effective actions giving rise to simple Ward identities. Within this method, we calculate the quantities that have been treated in…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
It seems that the literature suggests to go in two opposing directions simultaneously. On the one hand, many papers construct basis-independent quantities, since exactly these quantities appear in the expressions for observables. This means…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
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…
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
Neural radiance fields, or NeRF, represent a breakthrough in the field of novel view synthesis and 3D modeling of complex scenes from multi-view image collections. Numerous recent works have shown the importance of making NeRF models more…