The Slater sum of a quantum electron gas is put into the form of a Boltzmann factor. The exponent of this factor is approximated as a sum of pair functions. Well-known techniques are then applied to obtain approximate radial distribution functions for the quantum system. Expressions for the energy and pressure at any temperature and density are derived. A comparison is made with the ground-state energies obtained by other authors. This comparison indicates that the method should be accurate to within a few percent over a wide range of densities including the metallic region.

Comparisons are made between solutions to the Born-Green integral equation and radial distribution functions obtained by the Monte Carlo method by Wood and Parker for the Lennard-Jones potential. It is observed that multiplying the particle separation distance in the Born-Green case by a constant factor improves the agreement for loops beyond the first.

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A formalism is presented giving the development of $(z) in timc nith the interprctation that $(2) is the probability amplitude for observing an event at a space-time point 2. No properties other than the four spacetime coordinates are associated with an cvcnt. A Hilbert space is defined in which $(Z) is the result of a scalar product. The space-time position operators defined in this Hilbert space have no association with particle properties, such as mass. These operators cannot be defined in the Hilbert space spanned by solutions of a Schrodinger equation, since the operators lead out of the Hilbert subspace belonging to a given mass.I t is shown that state vectors in Hilbert space that are eigenvectors of P,Pp produce position amplitudes satisfying the Klein-Gordon equation. The relation between this Hilbert space and the one introduced by Dirac is discussed. Spin is not considered.

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