  Bose-Einstein momentum correlation functions of identical bosons reveal the
shape and size of the (soft) particle emitting source of the given particle.
The widths of these correlation functions are called HBT radii, named after
Brown and Twiss who studied the angular diameter of stars via intensity
correlations in their radio telescopes. Today, high energy physics experiments
measure the HBT radii as a function of many parameters: particle type,
transverse momentum, azimuthal angle, collision energy, collision geometry. In
this paper we present results from the RHIC PHENIX experiment. These include
the observation of strong azimuthal-angle dependence of the extracted Gaussian
HBT radii, the similarities and differences between kaon and pion HBT radii.
The key point of this paper is the application of Bose-Einstein correlations to
the search for the critical point: how HBT radii would show the appearance of a
first order phase transition, and what the non-monotonic collision energy
dependence of the pion source tells us about the critical point; and how the
non-Gaussian shape of correlation functions is related to one of the critical
exponents.
