  We investigate the many-body properties of a two-dimensional electron gas
constrained to the surface of a sphere, a system which is physically realized
in multielectron bubbles in liquid helium. A second-quantization formalism,
suited for the treatment of a spherical two-dimensional electron gas (S2DEG),
is introduced. Within this formalism, the dielectric response properties of the
S2DEG are derived, and we identify both collective excitations and a spectrum
of single-particle excitations. We find that the single-particle excitations
are constrained to a well-defined region in the angular momentum - energy
plane. The collective excitations differ in two important aspects from those of
a flat 2DEG: on a sphere, the 'spherical plasmons' have a discrete frequency
spectrum and the lowest frequency is nonzero.
