Related papers: On inserter regularization method
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
We analyze the large-order behaviour in perturbation theory of classes of diagrams with an arbitrary number of chains (i.e. photon lines, dressed by vacuum polarization insertions). We derive explicit formulae for the leading and subleading…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
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…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
Despite its simplicity, the unitary gauge is not a popular choice for practical loop calculations in gauge theories, due to the lack of off-shell renormalizability. We study the renormalization properties of the off-shell Green functions of…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered with…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
Taking the induced action for gauge fields coupled to affine currents as an example, we show how loop calculations in non-local two-dimensional field theories can be regulated. Our regularisation method for one loop is based on the method…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
The perturbative construction of the S-matrix in the causal spacetime approach of Epstein and Glaser may be interpreted as a method of regularization for divergent Feynman diagrams. The results of any method of regularization must be…
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…