  The diagonal representation and optical equivalence theorem are the E. C. G.
Sudarshan's mid 20th century adventures in non-classical optics. It basically
deals with a quantum mechanical description of photons to explain the quantum
properties of light. Inspired by Sudarshan's pioneering work we try to explain
the every minute mathematical details of his paper "Equivalence of
semi-classical and quantum mechanical descriptions of statistical light beams".
In this article we are going to go through some of the basics in developing
quantum optics, then land up in E.C.G's original work and try to present it as
rigorous as possible. We show some of its important applications in various
classes of physics problems.
