Bøger i Theoretical and Mathematical Physics serien

This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories.The book is targeted to researchers and graduate students.

This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts:Part One: Classical Dynamical SystemsAddresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity.Includes a survey of the theory of simple perceptrons and their storage capacity.Part Two: Quantum Dynamical SystemsFocuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems.Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom.Introduces a model ofquantum perceptron whose storage capacity is computed and compared with the classical one.Part Three: Quantum Dynamical Entropies and ComplexitiesDevoted to quantum dynamical entropies and algorithmic complexities.This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.