Mathematical theory of Feynman path integrals (Lecture notes in mathematics ; 523)

Science & Math

Albeverio, Sergio

Høegh-Krohn, Raphael

Mathematics

Springer

Imaging for Forensics and Security: From Theory to Practice provides a detailed analysis of new imaging and pattern recognition techniques for the understanding and deployment of biometrics and forensic techniques as practical solutions to increase security. It contains a collection of the recent advances in the technology ranging from theory, design, and implementation to performance evaluation of biometric and forensic systems. This book also contains new methods such as the multiscale approach, directional filter bank, and wavelet maxima for the development of practical solutions to biometric problems. The book introduces a new forensic system based on shoeprint imagery with advanced techniques for use in forensics applications. It also presents the concept of protecting the originality of biometric images stored in databases against intentional and unintentional attacks and fraud detection data in order to further increase the security.

Feynman path integrals: Proceedings, of the international colloquium held in Marseille 1978 (Lecture notes in physics)

Computers & Technology

Computer Science

Springer, Verlag

Stochastic processes, mathematics and physics: Proceedings of the 1st BiBos-Symposium, held in Bielefeld, West Germany, September 10-15, 1984 (Lecture notes in mathematics)

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

Solvable Models in Quantum Mechanics (Texts & Monographs in Physics)

H. Holden

F. Gesztesy

R Hoegh-Krohn

Physics

The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The first half presents a complete and self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics. The text's opening chapters introduce all of the material needed later, including a nonstandard development of the calculus, aspects of singular perturbation theory related to ordinary differential equations, and applications to topology and functional analysis. A significant portion of the text focuses on applications of nonstandard analysis to probability theory. Starting with nonstandard measure theory, the treatment advances to probability problems that can be represented by hyperfinite nonstandard models. Applications of nonstandard analysis to stochastic processes are treated at length, and the authors present numerous applications to mathematical physics. Additional topics include hyperfinite Dirichlet forms and Markov processes, differential operators, and hyperfinite lattice models.

Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Dover Books on Mathematics)

Fenstad, Jens Erik

Lindstrøm, Tom

Dover Publications

Classical string theory is concerned with the propagation of classical one-dimensional curves, i.e. "strings", and 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-Moody and Virasoro algebras has been used for such quantization. In this book, the authors give an introduction to global analytic and probabilistic aspects of string theory, bringing together and making explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.

A Mathematical Introduction to String Theory: Variational Problems, Geometric and Probabilistic Methods (London Mathematical Society Lecture Note Series 225)

Jost, Jürgen

Paycha, Sylvie

Scarlatti, Sergio

Cambridge University Press

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 stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.

Noncommutative Distributions: Unitary Representation of Gauge Groups and Algebras (Chapman & Hall/CRC Pure and Applied Mathematics)

Hoegh-Krohn, Raphael J.

Marion, Jean A.

Testard, D.

Torresani, B.

CRC-Press

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

Solvable Models in Quantum Mechanics (Theoretical and Mathematical Physics)

Gesztesy, Friedrich

Holden, H.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Mathematical Theory of Feynman Path Integrals: An Introduction (Lecture Notes in Mathematics, 523)

Mazzucchi, Sonia

Høegh-Krohn, Rafael

This monograph covers the theory of Dirichlet forms. It examines the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes and summarizes the model-theoretic genericity of hyperfinite stochastic processes theory.

Hyperfinite Dirichlet Forms and Stochastic Processes (Lecture Notes of the Unione Matematica Italiana, Vol. 10)

Herzberg, Frederik S.

Fan, Ruzong

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