  The elucidation of Landau Fermi liquid quasi-particles and their absence in
strongly correlated electron systems lies at the heart of modern research on
the quantum mechanics of electrons in condensed matter. Photoemission
spectroscopy of the single particle spectral function is a central experimental
tool for such studies. A general paradigm of quasi-particle formation is the
Fermi level resonance associated with the Kondo physics of the Anderson
impurity model, an effective self consisent version of which is utilized in
dynamic mean field theories of general lattice systems which may or may not
literally display Kondo physics. A general paradigm of quasi-particle absence
is the Luttinger liquid physics of the Tomonaga-Luttinger model. This paper
presents an overview of the theoretical ideas and shows examples in
photoemission spectra, taken from the work of the author and his collaborators,
of quasi-particle formation in impurity and lattice Kondo and non-Kondo
correlated electron systems, contrasted with quasi-particle absence in a
quasi-one-dimensional system.
