相关论文: Non-perturbative regularization and renormalizatio…

In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…

Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure…

The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…

We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\delta$ functions. We also discuss…

Dimensional regularization is applied to the computation of the gravitational wave field generated by compact binaries at the third post-Newtonian (3PN) approximation. We generalize the wave generation formalism from isolated post-Newtonian…

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…

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…

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory…

As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…

Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this…

In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function in the complement of that set. In particular, we establish a…

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic…

Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are…

On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field…

Although quantization has emerged as a promising approach to reducing computational complexity across various high-level vision tasks, it inevitably leads to accuracy loss in image super-resolution (SR) networks. This is due to the…

We derive a new class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop…

We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse CDF. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a…

Calculations of the two-loop $\beta$-function for N=1 supersymmetric electrodynamics are compared for regularizations by higher derivatives and by the dimensional reduction. The renormalized effective action are found to be the same for…