  In this Letter, we derive a quantum nonlinear sigma model (QNLSM) for quantum
Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit
of the low temperature is naturally carried out for the reliability of the
QNLSM. The S dependence of the effective coupling constant and the spin wave
velocity in the QNLSM are also obtained explicitly. The resulting spin wave
velocity for 2-dim spin-1/2 QHA highly concurs with the experimental data of
high $T_c$ compound La2CuO4. The predicted correlation lengths for 2d QHA and
spin-gap magnitudes for 1d QHA also agrees with the accurate numerical results.
