相关论文: Comparing Implicit, Differential, Dimensional and …
We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$ tensors and the $\gamma_5$ matrix, in implicit gauge-invariant regularization/renormalization methods defined in fixed integer dimensions. They include constrained…
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…
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…
We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG…
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…
We investigate the possibility of generalizing differential renormalization of D.Z.Freedman, K.Johnson and J.I.Latorre in an invariant fashion to theories with infrared divergencies via an infrared $\tilde{R}$ operation. Two-dimensional…
We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied straightforwardly to multi-loop…
Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional…
The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of…
We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of $X$. We conjecture and provide empirical and theoretical evidence that with small enough…
Recent progress in the understanding of vacuum expectation values and of infrared divergences in different regularization schemes is reviewed. Vacuum expectation values are gauge and renormalization-scheme dependent quantities. Using a…
For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional…
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…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
We propose a general quantum Hamiltonian formalism of a renormalization group (RG) flow with an emphasis on generalized symmetry by interpreting the elementary relationship between homomorphism, quotient ring, and projection. In our…
The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an…
The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…