Quantum Theory

An expert researcher argues for a revolutionary new understanding of quantum mechanics

Bohr and Planck helped shaped the cultural landscape of the world today. Now their work is available here in a digestible, pocket format for the modern reader.

An expert researcher argues for a revolutionary new understanding of quantum mechanics

Intended for graduate students in physics and related fields, this text is a self contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green's functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero- temperature perturbation theory, and the Matsubara, Keldysh, and Nambu -Gor'kov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable the student to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume, and which therefore provides an ideal testing ground for many-body theories. The book begins by introducing the Green's function for one-particle systems (using Feynman path integrals), general perturbation theory, and second quantization.

Nowadays it is becoming clearer and clearer that, in the description of natural phenomena, the triadic scheme - microseopie, mesoscopic, macroscopic - is only a rough approximation and that there are many levels of description, probably an infinite hierarchy, in which the specific properties of a given level express some kind of cumulative or collective behaviour of properties or sys­ tems corresponding to the lower levels. One of the most interesting challenges for contemporary natural sciences is the comprehension of the connections among these different levels of description of reality and the deduction of the laws of higher levels in this hierarchy from basic laws corresponding to lower levels. Since these cumulative or collective phenomena are, typically, nonlin­ ear effects, the transition from this general program to concrete scientific achievements requires the developement of techniques which allow physical information to be extracted from nonlinear quantum systems. Explicitly in­ tegrable examples of such systems are rare, and the most interesting physical phenomena are not captured by them. Even in the case of linear systems the fact that an explicit solution is formally available is often useless, since it is impossible to interpret interesting physical phenomena from it.

The goal of this monograph is to summarize the different quantum­ mechanical methods developed in the last 20 years to treat the electronic structure of polymers. Owing to the nature of the problem, these methods consist of a mixture of quantum-chemical and solid-state physical tech­ niques. The theory described in Part I treats, besides the Hartree-Fock problem, the· electron correlation, and it has also been developed for disordered polymeric systems. Though for obvious reasons the book could not include all the existing calculations, each new method des­ cribed is illustrated by a few applications, with a discussion of the numerical results obtained. Far more details see the Introduction to Part I. The second part contains the theoretical calculation of different properties of polymers based on the methods systematically introduced in the first part. The properties calculated include the electronic and vibrational spectra of polymers, and the computation of their transport, magnetic, and mechanical properties. In cases where reliable ex­ perimental data are available, the theoretical results are compared with them.

Volume 5 has three parts, dealing with General Relativity, Epistemological Issues, and Quantum Mechanics. The core of the first part is Hilbert’s two semester lecture course on ‘The Foundations of Physics’ (1916/17). This is framed by Hilbert’s published ‘First and Second Communications’ on the ‘Foundations of Physics’ (1915, 1917) and by a selection of documents dealing with more specific topics like ‘The Principle of Causality’ or a lecture on the new concepts of space and time held in Bucharest in 1918. The epistemological issues concern the intricate relation between nature and mathematical knowledge, in particular the question of irreversibility and objectivity (1921) as well as the subtle question whether what Hilbert calls the ‘world equations’ are physically complete (1923). The last part deals with quantum theory in its early, advanced and mature stages. Hilbert held lecture courses on the mathematical foundations of quantum theory twice, before and after the breakthrough in 1926. These documents bear witness to one of the most dramatic changes in the foundations of science.

The goal of this monograph is to summarize the different quantum­ mechanical methods developed in the last 20 years to treat the electronic structure of polymers. Owing to the nature of the problem, these methods consist of a mixture of quantum-chemical and solid-state physical tech­ niques. The theory described in Part I treats, besides the Hartree-Fock problem, the· electron correlation, and it has also been developed for disordered polymeric systems. Though for obvious reasons the book could not include all the existing calculations, each new method des­ cribed is illustrated by a few applications, with a discussion of the numerical results obtained. Far more details see the Introduction to Part I. The second part contains the theoretical calculation of different properties of polymers based on the methods systematically introduced in the first part. The properties calculated include the electronic and vibrational spectra of polymers, and the computation of their transport, magnetic, and mechanical properties. In cases where reliable ex­ perimental data are available, the theoretical results are compared with them.

Volume 5 has three parts, dealing with General Relativity, Epistemological Issues, and Quantum Mechanics. The core of the first part is Hilbert’s two semester lecture course on ‘The Foundations of Physics’ (1916/17). This is framed by Hilbert’s published ‘First and Second Communications’ on the ‘Foundations of Physics’ (1915, 1917) and by a selection of documents dealing with more specific topics like ‘The Principle of Causality’ or a lecture on the new concepts of space and time held in Bucharest in 1918. The epistemological issues concern the intricate relation between nature and mathematical knowledge, in particular the question of irreversibility and objectivity (1921) as well as the subtle question whether what Hilbert calls the ‘world equations’ are physically complete (1923). The last part deals with quantum theory in its early, advanced and mature stages. Hilbert held lecture courses on the mathematical foundations of quantum theory twice, before and after the breakthrough in 1926. These documents bear witness to one of the most dramatic changes in the foundations of science.