  The history of star formation in the strong gravitational potential of the
Galactic center has been of much interest, recently. We propose that the
sub-parsec-scale disk of massive stars orbiting the massive black hole at the
Galactic center can be interpreted in terms of partial accretion of extended
Galactic center clouds, such as the 50 \kms molecular cloud, as these clouds
envelop Sgr A* on their passage through the inner Galactic center. The loss of
angular momentum of the captured cloud material by self-interaction subsequent
to gravitationally focusing by Sgr A* naturally creates a compact gaseous disk
of material close to Sgr A* in which star formation takes place. On a larger
scale the formation of massive clusters such as the Arches and Quintuplet
clusters or on-going massive star formation such as Sgr B2 could also be
triggered by cloud-cloud collisions due to gravitational focusing in the deep
potential of the central bulge.
  Unlike the violent and high-pressure environment of clustered star formation
triggered by cloud-cloud collision, there are also isolated pockets of star
formation and quiescent dense clouds. These sites suggest an inefficient, slow
mode of star formation. We propose enhanced cosmic rays in the nuclear disk may
be responsible for inhibiting the process of star formation in this region. In
particular, we argue that the enhanced ionization rate due to the impact of
cosmic-ray particles is responsible for lowering the efficiency of on-going
star formation in the nuclear disk of our Galaxy. The higher ionization
fraction and higher thermal energy due to the impact of these electrons may
also reduce MHD wave damping which contributes to the persistence of the high
velocity dispersion of the molecular gas in the nuclear disk.
