Preface
The present book is based on a one-year course of lectures given intermittently
during the years from 1990 to 2010 at the University of Heidelberg. The lectures
were devised as an in-depth introduction into many-body theory for finite electronic
systems, that is, molecules, atoms, and clusters, addressing graduate, doctoral, and
postdoctoral students, who were generally interested in quantum-chemical methods
and computations. The original course is essentially covered by the first 10 chapters, while 7 additional chapters address further elaborations and extensions.
Many-body methods, or more accurately, field-theoretical many-body methods,
have originated in quantum field theory where they were developed as a means to
treat the physics of elementary particles. As was soon realized, these methods could
be transferred to the treatment of quantum many-body systems in solid-state physics and statistics, not conveying novel physics here but supplying a powerful new
formalism and a route toward alternative computational methods. Shortly afterward,
this formalism was taken up in the treatment of finite particle systems, first in
nuclear physics, and finally in quantum chemistry as well. It is now almost half a
century since computational schemes based on field-theoretical many-body theory
were developed and successfully applied to finite electronic systems.
In the field-theoretical approach, the many-particle problem is formulated in
terms of many-body Green’s functions or propagators. These entities are defined as
ground-state expectation values of time-dependent operator products, which, in
energy representation, take on the form of matrix elements of many-body resolvent
operators. They allow for a direct access to the energies and transition moments of
generalized excitation processes in the considered system, such as ionization
(electron removal), affinities (electron attachment), and neutral electronic excitation.
What is the advantage inherent to these methods and what can they actually do
better than the conventional procedures in dealing with small, medium size, and
large molecules? An apparent advantage is a direct access to physically relevant
quantities such as excitation energies and transition moments, which otherwise have
to be assembled from independent computations for the initial ground and final
excited states. But there is another, deeper justification, related to characteristic
shortcomings in the conventional approach.
v
The present book is based on a one-year course of lectures given intermittently
during the years from 1990 to 2010 at the University of Heidelberg. The lectures
were devised as an in-depth introduction into many-body theory for finite electronic
systems, that is, molecules, atoms, and clusters, addressing graduate, doctoral, and
postdoctoral students, who were generally interested in quantum-chemical methods
and computations. The original course is essentially covered by the first 10 chapters, while 7 additional chapters address further elaborations and extensions.
Many-body methods, or more accurately, field-theoretical many-body methods,
have originated in quantum field theory where they were developed as a means to
treat the physics of elementary particles. As was soon realized, these methods could
be transferred to the treatment of quantum many-body systems in solid-state physics and statistics, not conveying novel physics here but supplying a powerful new
formalism and a route toward alternative computational methods. Shortly afterward,
this formalism was taken up in the treatment of finite particle systems, first in
nuclear physics, and finally in quantum chemistry as well. It is now almost half a
century since computational schemes based on field-theoretical many-body theory
were developed and successfully applied to finite electronic systems.
In the field-theoretical approach, the many-particle problem is formulated in
terms of many-body Green’s functions or propagators. These entities are defined as
ground-state expectation values of time-dependent operator products, which, in
energy representation, take on the form of matrix elements of many-body resolvent
operators. They allow for a direct access to the energies and transition moments of
generalized excitation processes in the considered system, such as ionization
(electron removal), affinities (electron attachment), and neutral electronic excitation.
What is the advantage inherent to these methods and what can they actually do
better than the conventional procedures in dealing with small, medium size, and
large molecules? An apparent advantage is a direct access to physically relevant
quantities such as excitation energies and transition moments, which otherwise have
to be assembled from independent computations for the initial ground and final
excited states. But there is another, deeper justification, related to characteristic
shortcomings in the conventional approach.
v