The operator algebra and an identity in the statistical mechanics of fluids are used to demonstrate that the cumulant average of arbitrary products of appropriate combinations of local fluctuating energy and density are scale and conformal covariant at the critical point. These combinations are uncorrelated and are found by diagonalizing a matrix whose elements are energy and density derivatives of pressure-density and pressure-energy correlations. The eigenvalues are the dimensions of the appropriate variables.

• Received 6 August 1973

DOI:https://doi.org/10.1103/PhysRevLett.31.1193