Hartree--Fock Theory, Lieb's Variational Principle, and their Generalizations

TL;DR

This paper reviews Hartree--Fock theory in quantum mechanics, its generalizations, and significance in predicting symmetry breaking, highlighting its evolution from early proposals to modern applications.

Contribution

It provides a comprehensive overview of Hartree--Fock theory, including recent generalizations and their role in understanding symmetry phenomena in quantum systems.

Findings

Hartree--Fock theory has evolved significantly since its inception.

Generalizations of Hartree--Fock theory enhance its predictive power.

The theory is crucial for understanding symmetry breaking in quantum systems.

Abstract

Hartree--Fock theory in quantum mechanics is reviewed, from the proposal of the Hartree--Fock approximation right after quantum mechanics was formulated to its applications in modern physics. This includes the description of traditional Hartree--Fock theory in quantum chemistry, its generalizations of various kinds, and its importance for predicting the presence of symmetry breaking, or the absence thereof.