Ground state of many-electron systems based on the action function

The Hilbert space for an interacting electron system increases exponentially with electron number $N$. This limits the concept of wavefunctions $ψ$ based on solutions of the Schrödinger equation to $N \leq N_0$ with $N_0 \simeq 10^3$ \cite{Kohn1999}. It is argued that this exponential wall problem (EWP) is connected with an increasing redundance of information contained, e.g., in the ground-state of the system and it's wavefunction. The EWP as well as redundance of information are avoided when the characterization of the ground state is based on the action function $R$ rather than on the solutions $ψ$ of the Schödinger equation. Both are related through a logarithm, i.e., $R = -i \hbar \ ln ψ$. Working with the logarithm is made possible by the use of cumulants. It is pointed out the way electronic structure calculations for periodic solids may use this concept.

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