Algebraic Approach to the Many-Electron Problem

This book presents an algebraic approach to the coupled cluster method for many-electron systems, pioneered by Josef Paldus. Using field methods along with an algebraic, rather than diagrammatic, approach facilitates a way of deriving the coupled cluster method which is readily understandable at the graduate level. The book begins with the notion of the quantized electron field and shows how the N-electron Hamiltonian can be expressed in its language. This is followed by introduction of the Fermi vacuum and derivation of the Hartree-Fock equations along with conditions for stability of their solutions. Following this groundwork, the book discusses a method of configuration interaction to account for dynamical correlations between electrons, pointing out the size-extensivity problem, and showing how this problem is solved with the coupled cluster approach. This is followed by derivation of the coupled cluster equations in spin-orbital form. Finally, the book explores practical aspects, showing how one may take advantage of permutational and spin symmetries, and how to solve coupled-cluster equations, illustrated by the Hubbard model of benzene, the simplest quasi-realistic model of electron correlation.

Jaroslav Zamastil is an Associate Professor of theoretical physics at Charles University in Prague, Faculty of Mathematics and Physics. He teaches courses on undergraduate quantum mechanics, quantum electrodynamics, and field-theoretical methods in many-body problems. He conducts research in atomic and mathematical physics, and has published about 30 original scientific papers. He is the author of two previous books, Quantum Mechanics and Electrodynamics (Springer, 2017, co-authored with Jakub Benda, and originally published in Czech by Karolinum, 2016) and Understanding the Path from Classical to Quantum Mechanics (Springer, 2023).