Quantum Averages over the Ground State and the Gell–Mann–Low Theorem

This chapter considers the expectation value of an operator (or of products of two operators) over the ground state of the interacting system, when the time-dependent part of the Hamiltonian is switched off. These limitations apply to systems in equilibrium at zero temperature, which include important cases like insulators and semiconductors as well as Fermi liquids, for which the energy gap and the Fermi energy are, respectively, much larger than the available thermal energy. The ensuing formalism for ground-state averages at zero temperature relies on an “adiabatic assumption,” which cannot be applied as it is when excited states are involved in the ensemble averages.