The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.

This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the...

Operads provide a universal language to relate several disciplines in mathematics and physics. This book focuses on the striking relation between algebra, topology and string theory that is mediated by operads of graphs and surfaces in their role as a model of the correlation functions of quantum field theory.

Brings together, in an introductory form, the scattered material in the field of stochastic processes and statistical physics. This book is intended for undergraduate and graduate students of physics who wish to gain an introduction to stochastic, kinetic and nonequilibrium processes.

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