Summary of the Main Theses of This Book

V. M. Kenkre

Michael Berry

Roger Penrose has provoked a great deal of discussion and controversy with his recent book The Emperor's New Mind(Oxford University Press 1989). (For a summary and review of the book's arguments by Frank Tipler, see Physics World, November 1989, p45) Its main proposal is that three problems which are usually regarded as separate are actually part of the same problem, and so might eventually find a common solution.

R. Citro, Ferdinando Mancini

Kevin S. Bedell

The Fermi liquid theory was first introduced by Landau in 1956 to provide a theoretical basis for the properties of strongly correlated Fermi systems. This theory has proven to be crucial for our understanding of a broad range of materials. These include liquid [sup 3]He, [sup 3]He-[sup 4]He mixtures, simple metals, heavy-fermions, and nuclear matter to name a few. In the high temperature superconductors questions have been raised regarding the applicability of Fermi liquid theory to the normal state behavior of these materials. I will not address this issue in these lectures. My focus will be to summarize the foundations of this theory and to explore the consequences. These lectures are in part a summary of the excellent review article by Baym and Pethick and the books by Pines and Nozieres and Baym and Pethick. They include as well a summary of some articles that I have authored and co-authored. In the main body of the lectures I will not make any additional references to the books or articles. In the absence of reading the original materials, my lectures should provide the essentials of a mini-course in Fermi liquid theory.

Vasil Penchev

The book is devoted to the contemporary stage of quantum mechanics – quantum information, and especially to its philosophical interpretation and comprehension: the first one of a series monographs about the philosophy of quantum information. The second will consider Be l l ’ s inequalities, their modified variants and similar to them relations. The beginning of quantum information was in the thirties of the last century. Its speed development has started over the last two decades. The main phenomenon is entanglement. The subareas are quantum computer, quantum communication (and teleportation), and quantum cryptography. The book offers the following main conceptions, theses and hypotheses: – dualistic Phythagoreanism as a new kind among the interpretations of quantum mechanics and information: arithmetical, logical, and metamathematical one; – Gödel ’ s first incompleteness theorem is an undecidable proposition, and consequently the second one,too. – a partial rehabilitation of Hilbert ’ s program for the self-foundation of mathematics; – the dual-foundation of mathematics; – Skolemian relativity between: Cantor ’s kinds of infinity, finiteness and infinity, discreteness and continuity, completeness and incompleteness, etc.; – information is a physical quantity representing the non-reducibility of a system to its parts, particularly nonaddtivity; – there exist pure relations «by itself», which cannot be reduced to predications; – energy conservation can and should be generalized; – Einstein’ s «general covariance» or «principle of relativity» can and should be generalized to cover discrete morphisms where the notion of velocity does not make sense.