  We present a promising mode coupling theory study for the relaxation and
glassy dynamics of a system of strongly interacting self-propelled particles,
wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored
noise and thermal noises are included. Our starting point is an effective
Smoluchowski equation governing the distribution function of particle's
positions, from which we derive a memory function equation for the time
dependence of density fluctuations in nonequilibrium steady states. With the
basic assumption of absence of macroscopic currents and standard mode coupling
approximation, we can obtain expressions for the irreducible memory function
and other relevant dynamic terms. With these equations obtained, we study the
glassy dynamics of this thermal self-propelled particles system by
investigating the Debye-Waller factor f_{q} and relaxation time \tau_{\alpha}
as functions of the persistence time \tau_{p} of self-propulsion, the single
particle effective temperature T_{\text{eff}} as well as the number density
\rho. Consequently, we find the critical density \rho_{c} for given \tau_{p}
shifts to larger values with increasing magnitude of propulsion force or
effective temperature, in good accordance with previous reported simulation
works. In addition, the theory facilitates us to study the critical effective
temperature T_{\text{eff}}^{c} for fixed \rho as well as its dependence on
\tau_{p}. We find that T_{\text{eff}}^{c} increases with \tau_{p} and in the
limit \tau_{p}\to0, it approaches the value for a simple passive Brownian
system as expected. Our theory also well recovers the results for passive
systems and can be easily extended to more complex systems such as
active-passive mixtures.
