Hikoya Kasari

On the Breit equation

Abstract Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of the Schodinger case in the non-relativistic limit.

Eigenvalues of the Breit equation

Eigenvalues of the Breit Equation {eqnarray*} [(\vec{\alpha}_{1} \vec{p} + \beta_{1}m)_{\alpha \alpha^{\prime}} \delta_{\beta \beta^{\prime}} + \delta_{\alpha \alpha^{\prime}} (-\vec{\alpha}_{2} \vec{p} + \beta_{2}M)_{\beta \beta^{\prime}} - \frac{e^{2}}{r} \delta_{\alpha \alpha^{\prime}} \delta_{\beta \beta^{\prime}}] \Psi_{\alpha^{\prime} \beta^{\prime}} = E \Psi_{\alpha \beta}, {eqnarray*} in which only the static Coulomb potential is considered, have been found. Here the detailed discussion on the simple caces,

INFLATION AND ACCELERATING UNIVERSE IN MODIFIED MODULAR INVARIANT SUPERGRAVITY

^{1}S_{0},\ m=M

The Breit Equation

and

The Time evolution of unstable particles

m \neq M

Reheating Temperature after Inflation in No-Scale Supergravity

is given deriving the exact energy eigenvalues. The

Inflation, Gravitino and Reheating in Modified Modular invariant Supergravity

\alpha^2

Dilatonic Inflation, Gravitino and Reheating in Modified Modular invariant Supergravity

expansion is used to find radial wave functions. The leading term is given by classical Coulomb wave function. The technique used here can be applied to other cases.

Ho\u{r}ava-Lifshitz Gravity on Primordial Black Holes

A method of explaining the recently observed acceleration of cosmic expansion as well as inflation in the early universe is presented within the same framework. The goal is to construct an inflation model based on supergravity and the slow-roll approximation (SRA) that both satisfactorily predicts observed inflationary parameters and at the same time explains the accelerated expansion of the universe. The model is based on a modification of string-based modular invariant supergravity previously proposed by the present authors. It realizes slow-roll inflation in the Einstein frame and is successful in explaining Wilkinson Microwave Anisotropy Probe (WMAP) observational data, through fine-tuning procedure of free parameters. The parameter dependence of the model is considered in detail in order to determine the range for which the SRA can be applied. Within the allowed range of parameter values, a vacuum energy of ~10-120 can be obtained, which coincides with the cosmological constant, and can play the role of dark energy in the universe. The calculated inflationary parameters fit very well to seven-year WMAP data. The ratio of the scalar and tensor power spectra is predicted to be r ~6.8 ×10-2, and this may soon be verified by observations by the Planck satellite. The non-Gaussianity parameter fNL is also estimated by the slow-roll parameters.

Supersymmetry Breaking and Gravitino Production after Inflation in Modular Invariant Supergravity

Contrary to the conventional view, the Breit equation can be solved.