ABSTRACT

This chapter considers the factors arising in the zero-temperature frequency representation for the ground state energy. The physical essence of the result, the relation between the symmetry of the non-interacting zero-temperature ground state and the exact ground state. The expectation value of an arbitrary product of operators in the Bose ground state cannot be separated into independent products of contractions and there is no zero-temperature Wick's theorem as in the Fermion case. The point at which our previous derivations for Fermions cannot be generalized to Bosons is the construction of a canonical transformation analogous to such that all the new annihilation operators annihilate the ground state. The Fermion minus signs combined with the factor of N from the color sums do just what is required to generate the correct Bose factors. Zero temperature theory is applied to the dilute Bose gas and to Fermions in one dimension interacting via δ-function forces.