  We solve the two-point function of the lowest dimensional scalar operator in
the critical $\phi^4$ theory on $4-\epsilon$ dimensional real projective space
in three different methods. The first is to use the conventional perturbation
theory, and the second is to impose the crosscap bootstrap equation, and the
third is to solve the Schwinger-Dyson equation under the assumption of
conformal invariance. We find that the three methods lead to mutually
consistent results but each has its own advantage.
