In this paper, some important many-body characteristics of H-shaped quantum wires are studied in the presence of external electric and magnetic fields within the Landau gauge. By introducing a mathematical definition of the H-shaped confinement potential, we calculate the profile of probability distribution of charge carriers in the ground and the first excited states. Our analysis shows that in the presence of external electric and magnetic fields, single-particle properties of carriers are sensitive functions of an asymmetric parameter that measures the relative width of the well in two transverse directions. We study the bandgap renormalization (BGR) effect in this quasi-one-dimensional system within the dynamical random phase GW approximation. We study also the effects of electric and magnetic fields on the values of the BGR. Application of the external fields leads to more renormalization of the fundamental gap both in the ground state and the first excited state. Then, we extend our study to incorporate the contribution of the first excited state wave function to this renormalization. We show that the absolute values of the bandgap narrowing in this case are larger than the corresponding renormalization calculated with only the ground state wave function.
