Encyclopedia of Mathematical Physics

The goal of this major undertaking is to support and enhance the interactions between mathematics and physics by making full use of the modern information technologies. Indeed, the 20th century was full of dramatic discoveries in each domain. And the important advances of that century in mathematical physics demonstrate clearly that physics is much closer to deep problems in mathematics than one could imagine by studying textbooks in our universities, and that physical ideas and concepts are often seminal in mathematics."The Modern Encyclopedia of Mathematical Physics" (MEMPhys) is a truly 21st century scientific encyclopedia, emphasizing mathematical physics as opposed to mathematics on one side and physics on the other. The central idea is to create a modern version of "Maimonides' Guide for the Perplexed", albeit limited to this multidisciplinary field. Indeed nowadays, increasingly so, the problem (especially in science) is not so much the existence or availability of information, but the ability to find, when the need occurs, pertinent and reliable information. So MEMPhys seeks to be a model for locating authoritative overviews and an efficient starting point for researchers and students at any level.Moreover, mathematical physics is not just an intersection of mathematics with physics, and certainly not a disjoint union of topics in both, but the discipline has an intrinsic value and existence that is articulated throughout this work. Accordingly, the contributions are written in precise mathematical language with clear indication of heuristic aspects, with physical interpretations or applications serving as examples. The ability to interrelate distinct items in MEMPhys (such as connecting an entry from the Encyclopedia with material from a handbook as well as with many texts existing in electronic form) enhance that characteristic of MEMPhys. Since this reference anticipates and seeks as wide a scientific audience as possible, students of mathematical physics, physics, and mathematics readily find concise summaries of recent profound ideas and to get a stimulating idea of their interrelations.

Table of Contents:
1. Algebra, Geometry and Analysis in Modern Mathematical Physics 1.1 Algebra 1.2 Geometry 1.3 Analysis 2. Dynamical systems in Mathematical Physics and Classical Mathematical Physics 2.1 Classical Mechanics 2.2 Dynamical Systems 2.3 Partial Differential Equations of classical 2.4 Mechanics of continuous medium/ continuum 3. Quantum Mechanics 3.1 Quantization 3.2 Spectral and scattering theories 3.3 Inverse scattering problems 3.4 Perturbative and asymptotic methods 3.5 Quantum dynamical systems 3.6 Open quantum systems 3.7 Random potentials 3.8 Measurements and quantum information 4. Quantum Field Theory 4.1 Fields, Symmetries and Lagrangians 4.2 Quantization 4.3 Axiomatic QFT 4.4 Perturbative QFT 4.5 Non-perturbative QFT 4.6 QFT on Manifolds and in External Fields 5. Statistical Physics 5.1 Equilibrium Statistical Mechanics 5.2 Nonequilibrium Statistical Mechanics 5.3 Condensed Matter and Solid States 5.4 Disordered systems 6. Integrable Systems 6.1 Classical Integrable Models 6.2 Quantum Integrable Models 6.3 Equations 6.4 Algebro-geometrical methods 7. Mathematical aspects of General Relativity 7.1 Exact solutions of the Einstein equations 7.2 Einstein's equations with matter 7.3 Hamiltonian method in General Relativity 7.4 Variation methods in General Relativity 7.5 Global methods and singularities theorems 7.6 Black Holes 7.7 Kaluza-Klein theories 7.8 Supergravity 7.9 Brane Worlds 7.10 Einstein-Cartan Theory 7.11 Spinors, spin coefficients, and twisters 7.12 Cosmology 7.13 Computational methods in general relativity - the theory 8. String Theory 8.1 Bosonic String 8.2 Superstring Theories, 5 Types of Superstrings 8.3 D-Branes 8.4 Dualities in String Theories 8.5 String Field Theories 8.6 Compactifications. 8.7 Topological Strings 8.8 M Theory 8.9 Phenomenology of String Theories

About the Author :
Dr. Irina Aref'eva will serve as Chief Executive Editor for The Modern Encyclopedia of Mathematical Physics (MEMPhys). She is professor at the Steklov Mathematical Institute Moscow, in the Department of Theoretical Physics. She is a colleague of Dr. L. Faddeev, who serves as editorial board member of the Springer journal Letters in Mathematical Physics.