  We present a theory for the dynamics of a binary mixture with particle size
swaps. The theory is based on a factorization approximation similar to that
employed in the mode-coupling theory of glassy dynamics. The theory shows that,
in accordance with physical intuition, particle size swaps open up an
additional channel for the relaxation of density fluctuations. Thus, allowing
swaps speeds up the dynamics and moves the dynamic glass transition towards
higher densities and/or lower temperatures. We calculate an approximate dynamic
glass transition phase diagram for an equimolar binary hard sphere mixture. We
find that in the presence of particle size swaps, with increasing ratio of the
hard sphere diameters the dynamic glass transition line moves towards higher
volume fractions, up to the ratio of the diameters approximately equal to 1.2,
and then saturates. We comment on the implications of our findings for the
theoretical description of the glass transition.
