  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.
