Title: Dressed Majorana fermion in a hybrid nanowire

Abstract: The low-energy theory of hybrid nanowire systems fails to define Majorana fermion (MF) in the strong tunneling and magnetic field strength. To address this limitation, we propose a holistic approach to define MF in which the quasi-excitation in nanowire and superconductor constitutes together its own ``antiparticles''. This definition is general, beyond the constraint presented in the low-energy theory. It reveals that the Majorana phase depends not only on the chemical potential and Zeeman energy in nanowire but also on those of superconductor, and that the mismatch of chemical potential leads not to observe MF. Such a broader perspective provides more specific experimental guidance under various conditions