  We introduce and analyze a novel mean-field model for polariton condensates
with velocity dependence of the effective polariton mass due the photon and
exciton components. The effective mass depends on the in-plane wave vector k,
which at the inflection point of the lower polariton energy branch becomes
infinite and above negative. The polariton condensate modes of the new
mean-field theory are now sensitive to mass variations and for certain points
of the energy dispersion the polariton condensate mode represents fractional
quantum mechanics. The impact of the generalized kinetic energy term is
elucidated by numerical studies in 1D and 2D showing significant differences
for large velocities. Analytical expressions for plane wave solutions as well
as a linear waves analysis show the significance of this new model.

Quantum Physics;Quantum Gases