By means of the finite temperature and finite density real time Green'
s function method, the effective mass of sigma meson is calculated by
summing the bubble diagrams. It is found that the formula of effective
mass given by rho meson can also be used to describe the sigma meson,
but the parameter n depends on density. The conjecture of Brown and R
ho about the effective mass of meson can well be proved by quantum fie
ld theory in high temperature region.