Related papers: Dimensional Regularization and Nuclear Potentials
We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…
The role of the delta isobar degrees of freedom in nucleon-nucleon scattering is revisited. We attempt to understand why the dimensionally regularized two-pion exchanges with the explicit delta isobar is much stronger than the ones with…
We present an integral density method for calculating the multifractal dimension spectrum for the nucleon distribution in atomic nuclei. This method is then applied to analyze the non-uniformity of the density distribution in several…
We study the one-dimensional contact process in its quantum version using a recently proposed real space renormalisation technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply…
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…
A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits to extract the interaction $V(\vec{r},\vec{p})$…
The matrix elements of relativistic nucleon-nucleon $(NN)$ potentials are calculated directly from the nonrelativistic potentials as a function of relative $NN$ momentum vectors, without using a partial wave decomposition. To this aim, the…
Guided by history, we review the major developments concerning realistic nucleon-nucleon (NN) potentials since the pioneering work by Kuo and Brown on the effective nuclear interaction. Our main emphasis is on the physics underlying various…
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 introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $\delta$-$\delta'$ interaction. After a simple general presentation in one dimension, we briefly discuss a…
We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is…
We use standard distorted wave theory techniques and dimensional regularization to find out solutions of the nucleon-nucleon Lippman--Schwinger equation with a kernel determined by the Weinberg's next-to-leading potential, which consists of…
Infinite nuclear matter is studied by resuming the series of ladder diagrams based on the results developed by us in Ann. Phys. 437, 168741 (2022). The master formula for the energy density is explicitly solved for the case of contact…
Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed…
We discuss the problem of renormalization of dynamical equations which arises in an effective field theory description of nuclear forces. By using a toy model of the separable NN potential leading to logarithmic singularities in the Born…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
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…
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a…
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit…
Non-differentiable potentials, such as the V-shaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouville-type interaction,…