Related papers: Numerical renormalization using dimensional regula…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
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…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
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 quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of…
In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
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…
When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an…
When homogenizing elliptic partial differential equations, the so-called corrector problem is pivotal to compute the macroscale effective coefficients from the microscale information. To solve this corrector problem in the periodic setting,…