Recent developments in theoretical physics include new instances of the unification of quite different phenomena. The theoretical community is challenged by the growing interactions between high-energy physics, statistical physics, and condensed matter physics. The common language, though, is exact solutions of two-dimensional and conformable field theories. This volume is a faithful representation of this interdisciplinary domain. Conformable and integrable field theories have been active research topics for several decades. The main recent developments concern the boundary effects and applications to disordered systems. The number of applications of the exact methods to condensed-matter problems has been growing over the years. Nowadays it is widely recognized that strongly interacting systems in low dimensions can be successfully described by integrable and conformable theories. This volume is an indispensable aid to those seeking to find their way in this domain.

This volume contains the invited contributions to the NATO Advanced Research Workshop on Integrable Quantum Field Theories held at the Villa Olmo, Como, Italy, September 14-18, 1992. About 70 researchers from all over world gathered at this in- terdisciplinary workshop, which turned out to be timely and very stimulating. We are grateful to the institutions that made it possible: the NATO Scientific Affairs Divi- sion, the Istituto Nazionale di Fisica Nucleare and the Scuola Internazionale Superiore di Studi Avanzati for financial support, and the Centro A.Volta for hospitality. In the past decades integrability was mostly explored in the framework of mathe- matical physics. However, in the last few years it has become a prominent subject in many domains of theoretical physics: two dimensional statistical mechanical models, two-dimensional conformal field theories and their perturbations, matrix models of two-dimensional gravity. This trend has been confirmed by the workshop: progress has been reported in all of the above topics both from physicists and mathematicians. One can recognize three broad groups of subjects: 1) 2D lattice models and off-critical solvable models, 2) Kac-Moody algebras and their role in integrable theories, 3) matrix models of string theory and their relation with topological and integrable field theories.

700 years after Dante Alighieri's death, this book intertwines the voice of the great poet with that of an exceptional contemporary, Marco Polo, who was equally curious about the geography of both earthly and celestial worlds. If Polo was the “ordinary genius� of the XIII century, the designation of “sorcerer genius� must go to Alighieri, the man with encyclopedic wisdom, at ease with his era’s philosophy, theology, and science. The sorcerer genius—well versed in this world—must create their own, which he did with The Divine Comedy. On the other hand, The Travels of Marco Polo, the greatest classic in travel literature, offers wonder and provides delight. This book combines the unforgettable characters of both books, the darkness of the infernal landscapes with the immensity of the Asian deserts, the richness of the Mongol empire with the glamor of medieval philosophy, the aspirations and dreams of two great explorers with knowledge of the science of their time, as well as the ever-eternal cosmology. This is an accessible and entertaining book for high school students, scholars of scientific history and the history of ideas, and curious readers who want to know more about Dante and Marco Polo and their unquenchable thirst for knowledge. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

This volume contains the invited contributions to the NATO Advanced Research Workshop on Integrable Quantum Field Theories held at the Villa Olmo, Como, Italy, September 14-18, 1992. About 70 researchers from all over world gathered at this in- terdisciplinary workshop, which turned out to be timely and very stimulating. We are grateful to the institutions that made it possible: the NATO Scientific Affairs Divi- sion, the Istituto Nazionale di Fisica Nucleare and the Scuola Internazionale Superiore di Studi Avanzati for financial support, and the Centro A.Volta for hospitality. In the past decades integrability was mostly explored in the framework of mathe- matical physics. However, in the last few years it has become a prominent subject in many domains of theoretical physics: two dimensional statistical mechanical models, two-dimensional conformal field theories and their perturbations, matrix models of two-dimensional gravity. This trend has been confirmed by the workshop: progress has been reported in all of the above topics both from physicists and mathematicians. One can recognize three broad groups of subjects: 1) 2D lattice models and off-critical solvable models, 2) Kac-Moody algebras and their role in integrable theories, 3) matrix models of string theory and their relation with topological and integrable field theories.

Recent developments in theoretical physics include new instances of the unification of quite different phenomena. The theoretical community is challenged by the growing interactions between high-energy physics, statistical physics, and condensed matter physics. The common language, though, is exact solutions of two-dimensional and conformable field theories. This volume is a faithful representation of this interdisciplinary domain. Conformable and integrable field theories have been active research topics for several decades. The main recent developments concern the boundary effects and applications to disordered systems. The number of applications of the exact methods to condensed-matter problems has been growing over the years. Nowadays it is widely recognized that strongly interacting systems in low dimensions can be successfully described by integrable and conformable theories. This volume is an indispensable aid to those seeking to find their way in this domain.

Science, with its inherent tension between the known and the unknown, is an inexhaustible mine of great stories. Collected here are twenty-six among the most enchanting tales, one for each letter of the alphabet: the main characters are scientists of the highest caliber most of whom, however, are unknown to the general public. This book goes from A to Z. The letter A stands for Abel, the great Norwegian mathematician, here involved in an elliptic thriller about a fundamental theorem of mathematics, while the letter Z refers to Absolute Zero, the ultimate and lowest temperature limit, - 273,15 degrees Celsius, a value that is tremendously cooler than the most remote corner of the Universe: the race to reach this final outpost of coldness is not yet complete, but, similarly to the history books of polar explorations at the beginning of the 20th century, its pages record successes, failures, fierce rivalries and tragic desperations. In between the A and the Z, the other letters of the alphabet are similar to the various stages of a very fascinating journey along the paths of science, a journey in the company of a very unique set of characters as eccentric and peculiar as those in Ulysses by James Joyce: the French astronomer who lost everything, even his mind, to chase the transits of Venus; the caustic Austrian scientist who, perfectly at ease with both the laws of psychoanalysis and quantum mechanics, revealed the hidden secrets of dreams and the periodic table of chemical elements; the young Indian astrophysicist who was the first to understand how a star dies, suffering the ferocious opposition of his mentor for this discovery. Or the Hungarian physicist who struggled with his melancholy in the shadows of the desert of Los Alamos; or the French scholar who was forced to hide her femininity behind a false identity so as to publish fundamental theorems on prime numbers. And so on and so forth. Twenty-six stories, which reveal the most authentic atmosphere of science and the lives of some of its main players: each story can be read in quite a short period of time -- basically the time it takes to get on and off the train between two metro stations. Largely independent from one another, these twenty-six stories make the book a harmonious polyphony of several voices: the reader can invent his/her own very personal order for the chapters simply by ordering the sequence of letters differently. For an elementary law of Mathematics, this can give rise to an astronomically large number of possible books -- all the same, but - then again - all different. This book is therefore the ideal companion for an infinite number of real or metaphoric journeys.

Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.