Related papers: From Dimensional to Cut-Off Regularization
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
Effective field theories (EFTs) require regularization and renormalization to gain predictive power. While regularization is inconsequential from the point of view of the observable predictions of EFT -- in a renormalized theory we expect…
A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…
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 non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with…
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,…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
We study the supersymmetric kink with higher derivative and momentum cut-off regularization schemes. We introduce the new momentum cut-off regularization scheme which we call ``generalized momentum cut-off''. A new, explicit computation for…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
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…
We study the solution of the relativistic Schr\"odinger equation for a point particle in 1-d under $\delta$-function potential by using cutoff regularization. We show that the problem is renormalizable, and the results are exactly the same…
The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
We show that the Pauli-Villars regularized action for a scalar field in a gravitational background in 1+1 dimensions has, for any value of the cutoff M, a symmetry which involves non-local transformations of the regulator field plus (local)…
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…
An implicit four dimensional regularization is applied to calculate the axial-vector-vector anomalous amplitude. The present technique always complies with results of Dimensional Regularization and can be easily applied to processes…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of gamma5. Also loop calculations in supersymmetric theories need a consistent definition of gamma5. In…
We derive one- and two-dimensional models for classical electromagnetism by making use of Hadamard's method of descent. Low-dimensional electromagnetism is conceived as a specialization of the higher dimensional one, in which the fields are…