  Collective (elementary) excitations of quantum bosonic condensates, including
condensates of exciton polaritons in semiconductor microcavities, are a
sensitive probe of interparticle interactions. In anisotropic microcavities
with momentum-dependent TE-TM splitting of the optical modes, the excitations
dispersions are predicted to be strongly anisotropic, which is a consequence of
the synthetic magnetic gauge field of the cavity, as well as the interplay
between different interaction strengths for polaritons in the singlet and
triplet spin configurations. Here, by directly measuring the dispersion of the
collective excitations in a high-density optically trapped exciton-polariton
condensate, we observe excellent agreement with the theoretical predictions for
spinor polariton excitations. We extract the inter- and intra-spin polariton
interaction constants and map out the characteristic spin textures in an
interacting spinor condensate of exciton polaritons.
