Quantization, nonlinear partial differential equations, and operator algebra : 1994 John von Neumann Symposium on Quantization and Nonlinear Wave Equations, June 7-11, 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts
著者
書誌事項
Quantization, nonlinear partial differential equations, and operator algebra : 1994 John von Neumann Symposium on Quantization and Nonlinear Wave Equations, June 7-11, 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts
（Proceedings of symposia in pure mathematics, v. 59）
American Mathematical Society, c1996
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注記
Includes bibliographical references
内容説明・目次
内容説明
Recent inroads in higher-dimensional nonlinear quantum field theory and in the global theory of relevant nonlinear wave equations have been accompanied by very interesting cognate developments. These developments include symplectic quantization theory on manifolds and in group representations, the operator algebraic implementation of quantum dynamics, and differential geometric, general relativistic, and purely algebraic aspects.""Quantization and Nonlinear Wave Equations"" thus was highly appropriate as the theme for the first John von Neumann Symposium (June 1994) held at MIT. The symposium was intended to treat topics of emerging signifigance underlying future mathematical developments. This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties.Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrodinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.
目次
$E_0$-semigroups in quantum field theory by W. Arveson Nonlinear phenomena in the spectral theory of geometric linear differential operators by T. Branson Existence theorem for solutions of Einstein's equations with 1 parametric spacelike isometry groups by Y. Choquet-Bruhat and V. Moncrief Quantum stochastic calculus, evolutions, and flows by R. L. Hudson Endomorphisms of $\mathcal B(\mathcal H)$ by O. Bratteli, P. T. Jorgensen, and G. L. Price Absolutely continuous spectrum in random Schrodinger operators by A. Klein Quantization by deformation and statistical mechanics by A. Lichnerowicz Possible classification of continuous spatial semigroups of *-endomorphisms of $\mathfrak B(\mathfrak h)$ by R. T. Powers Rigorous covariant form of the correspondence principle by I. Segal The relativistic Boltzmann equation by W. A. Strauss Microlocal analysis and nonlinear PDE by M. E. Taylor.
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