Transverse momentum and energy correlations in the equilibrium system from high-energy nuclear collisions

The so-called $\Phi$ parameter, which measures the transverse momentum or energy correlations (fluctuations) in high-energy collisions independently of the particle multiplicity, is computed for the equilibrium ideal gas. As expected $\Phi$ vanishes for the particles obeying Boltzmann statistics but is finite for the quantum particles, positive for bosons and negative for fermions. $\Phi_{p_{\perp}}$, which is found for the pions gas, significantly exceeds the value of $\Phi_{p_{\perp}}$ measured by the NA49 experiment. The discrepancy is discussed.