arXiv subjects

Masanobu Yahiro

Publications and source records attributed to Masanobu Yahiro.

129 records · Page 8Linked to original sources

arXiv1995

A perturbative renormalization group approach to light-front Hamiltonian

A perturbative renormalization group (RG) scheme for light-front Hamiltonian is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and applied to the simplest $ϕ^4$ model with spontaneous breaking of the $Z_2$ symmetry. RG equations are derived at one-loop order for both symmetric and broken phases. The equations are consistent with those calculated in the covariant perturbation theory. For the symmetric phase, an initial cutoff Hamiltonian in the RG procedure is made by excluding the zero mode from the canonical Hamiltonian with an appropriate regularization. An initial cutoff Hamiltonian for the broken phase is constructed by shifting $ϕ$ as $ϕ\rightarrowϕ-v$ in the initial Hamiltonian for the symmetric phase. The shifted value $v$ is determined on a renormalization trajectory. The minimum of the effective potential occurs on the trajectory.

hep-th↗

arXiv1994

Two-dimensional SU(N) Gauge Theory on the Light Cone

Two-dimensional SU($N$) gauge theory is accurately analyzed with the light-front Tamm-Dancoff approximation, both numerically and analytically. The light-front Einstein-Schrödinger equation for mesonic mass reduces to the 't Hooft equation in the large $N$ limit, $g^2N$ fixed, where $g$ is the coupling constant. Hadronic masses are numerically obtained in the region of $m^2 \ll g^2N$, where $m$ is the bare quark (q) mass. The lightest mesonic and baryonic states are almost in valence. The second lightest mesonic state is highly relativistic in the sense that it has a large 4-body ($ {\rm qq} \bar{\rm q} \bar{\rm q} $) component in addition to the valence (${\rm q} \bar{\rm q}$) one. In the strong coupling limit our results are consistent with the prediction of the bosonization for ratios of the lightest and second lightest mesonic masses to the lightest baryonic one. Analytic solutions to the lightest hadronic masses are obtained, with a reasonable approximation, as $\sqrt{2Cm}(1-1/N^2)^{1/4}$ in the mesonic case and $\sqrt{CmN(N-1)}(1-1/N^2)^{1/4}$ in the baryonic case, where $C=(g^2Nπ/6)^{1/2}$. The solutions well reproduce the numerical ones. The $N$- and $m$-dependences of the hadronic masses are explicitly shown by the analytical solutions.

hep-th↗

arXiv1993

The massive Schwinger model with $SU(2)_{f}$ on the light cone

The massive Schwinger model with two flavors is studied in the strong coupling region by using light-front Tamm-Dancoff approximation. The mass spectrum of the lightest particles is obtained numerically. We find that the mass of the lightest isotriplet (``pion'') behaves as $m^{0.50}$ for the strong couplings, where $m$ is the fermion mass. We also find that the lightest isosinglet is not in the valence state (``eta'') which is much heavier in the strong coupling region, but can be interpreted as a bound state of two pions. It is 1.762 times heavier than pion at $m=1.0\times10^{-3}(e/\sqrtπ)$, while Coleman predicted that the ratio is $\sqrt3$ in the strong coupling limit. The ``pion decay constant'' is calculated to be 0.3945.

hep-th↗