Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac ...
Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras. Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary ...
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low ...
Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of "Extreme Events in Nature and Society". The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling ...
Differential (and more general self-adjoint) operators involving singular interactions arise naturally in a range of topics such as, classical and quantum physics, chemistry, and electronics. This book presents a systematic mathematical study of these operators, with particular emphasis on spectral and scattering problems. Suitable for researchers ...
Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, ...
In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The ...
In October 1998 a conference was held in Lisbon to celebrate the 60th birthday of Ludwig Streit. This volume collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honour Ludwig Streit's scientific career and personality. The contributors cover many aspects of ...
Stochastic analysis is a field of mathematical research having numerous interactions with other domains of mathematics such as partial differential equations, Riemannian path spaces, dynamical systems, optimization. It also has many links with applications in engineering, finance, quantum physics, and other fields. This book covers recent and ...
As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is ...
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