  We have employed high resolution angle resolved photoemission spectroscopy
(ARPES) measurements to investigate many-body renormalizations of the
single-particle excitations in $1T$-TiSe$_2$. The energy distribution curves of
the ARPES data reveal intrinsic peak-dip-hump feature, while the electronic
dispersion derived from the momentum distribution curves of the data
highlights, for the first time, multiple kink structures. These are canonical
signatures of a coupling between the electronic degrees of freedom and some
Bosonic mode in the system. We demonstrate this using a model calculation of
the single-particle spectral function at the presence of an electron-Boson
coupling. From the self-energy analysis of our ARPES data, we discern some of
the critical energy scales of the involved Bosonic mode, which are $\sim$15 and
26 meV. Based on a comparison between these energies and the characteristic
energy scales of our Raman scattering data, we identify these Bosonic modes as
Raman active breathing (${\text{A}}_\text{1g}$) and shear
(${\text{E}}_\text{g}$) modes, respectively. Direct observation of the
band-renormalization due to electron-phonon coupling increases the possibility
that electron-phonon interactions are central to the collective quantum states
such as charge density wave (CDW) and superconductivity in the compounds based
on $1T$-TiSe$_2$.
