  I construct field theory on an evolving fuzzy two-sphere, which is based on
the idea of evolving non-commutative worlds of the previous paper. The
equations of motion are similar to the one that can be obtained by dropping the
time-derivative term of the equation derived some time ago by Banks, Peskin and
Susskind for pure-into-mixed-state evolutions. The equations do not contain an
explicit time, and therefore follow the spirit of the Wheeler-de Witt equation.
The basic properties of field theory such as action, gauge invariance and
charge and momentum conservation are studied. The continuum limit of the scalar
field theory shows that the background geometry of the corresponding continuum
theory is given by ds^2 = -dt^2+ t d Omega^2, which saturates locally the
cosmic holographic principle.
