2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....

2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....

A major task for theoretical chemists is the development of methods to predict energy differences with chemical accuracy. Most quantum chemists agree that accurate prediction of relative energies requires application of theories that include electron correlation effects, effects not treated in self-consistent-field (SCF) calculations [1-4]. Estimates of molecular correlation energy have been ob...

An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of quantum physics, many-body physics, physics of complex systems, and various aspects of applied physics and applied mathematics. A general approach for dealing wit...