Related papers: Perturbative Effective Theory in an Oscillator Bas…
This is the 4-th paper in the series devoted to a systematic study of the problem of mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of…
The internal structure of deuterons weakly influences a motion of their center of mass (translational motion). The scenario can be different when the translational wave function has a formal singularity along the line (thread) connecting…
Pionless effective field theory with dibaryon fields is reexamined for observables involving the deuteron. The electromagnetic form factors of the deuteron and the total cross sections of radiative neutron capture on the proton, $np \to…
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [x_i,p_j]=i hbar[(1+ beta p^2) delta_{ij} + beta' p_i p_j]. These…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
In the Schrodinger picture of the Dirac quantum mechanics, defined in charts with spatially flat Robertson-Walker metrics and Cartesian coordinates the perturbation theory is applied to the interacting part of the Hamiltonian operator…
An effective nucleon-nucleon interaction calculated in nuclear matter from the Bonn potential has been parametrized in terms of a local density- and energy-dependent two-body interaction. This allows to calculate the real part of the…
We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by…
These lectures introduce some of the basic notions of effective field theories, as used in particle physics. The topics discussed are the $\Delta S=1$ and $\Delta S =2$ weak interactions, and chiral perturbation theory as applied to mesons,…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
Effective Hamiltonians and effective electroweak operators are calculated with the Okubo-Lee-Suzuki formalism for two-nucleon systems. Working within a harmonic oscillator basis, first without and then with a confining harmonic oscillator…
We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking \Delta m^2_{21} / \Delta m^2_{31}, s_{13}, and the NSI elements \epsilon_{\alpha \beta}…
We present a new formulation of effective field theory for nucleon-nucleon (NN) interactions which treats pion interactions perturbatively, and we offer evidence that the expansion converges satisfactorily to third order in the expansion,…
Positivity constraints are derived on pion-nucleon scattering amplitudes and their even-order derivatives inside the Mandelstam Triangle with the help of dispersion relations. Fairly interesting constraints are obtained on some of the low…
One of the important features of nuclear forces is their strong repulsive nature at short ($\le 0.5-0.6$~Fm) distances which prevents atomic nuclei from collapsing, thus guarantying the stability for the visible matter. However the…
Nuclear effects in polarized inelastic electron scattering off polarized $^3He$ and polarized $^2H$ are discussed; in the resonance region, Fermi motion effects are found to be much larger than in deep inelastic scattering. It is shown that…
These lectures are a pedagogical -- not comprehensive -- introduction to the applications of effective field theory in the context of nuclear and atomic physics. A common feature of these applications is the interplay between…
Solutions to the nuclear many-body problem rely on effective interactions, and in general effective operators, to take into account effects not included in calculations. These include effects due to the truncation to finite model spaces…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…