  We derived the expression of the normalized $q$-expectation value based on the density operator to the order $1-q$ with the physical temperature in the Tsallis nonextensive statistics of entropic parameter $q$. With the derived expression of the normalized $q$-expectation value, we calculated the momentum distribution and the correlation to the order $1-q$ as functions of the inverse physical temperature for a free scalar field. To the order $1-q$, the momentum distribution derived by using the density operator coincides with the momentum distribution derived from the entropic measure described with the distribution, when the physical temperature equals the temperature in the distribution derived from the entropic measure. The correlation depends on the momentums for $q \neq 1$. The factor two appears in the correlation for the same momentums, and indicates that the effects of boson at $q \neq 1$ and those at $q=1$ are similar for the correlation. 
Momentum distribution and correlation for a free scalar field in the   Tsallis nonextensive statistics based on density operator