Cantitate/Preț
Produs
Total produse
Vezi coșul
Symplectic Geometry and Quantum Mechanics de Maurice A. de Gosson

Symplectic Geometry and Quantum Mechanics: Operator Theory: Advances and Applications, cartea 166

Autor Maurice A. de Gosson
en Limba Engleză Hardback – 18 mai 2006

Destinat nivelului de cercetare (doctorat și referință profesională), volumul de față reprezintă o sinteză riguroasă a procesului de „symplectizare” a fizicii, fenomen început în anii '70. Găsim în această carte o demonstrație clară a faptului că geometria symplectică nu este doar un instrument pentru mecanica clasică hamiltoniană, ci limbajul natural al mecanicii cuantice. Maurice A. de Gosson alege să lucreze aproape exclusiv în spațiul symplectic plat, o decizie pedagogică strategică ce permite cititorului să pătrundă în esența fenomenelor fără a fi blocat de formalismul excesiv al notațiilor intrinseci.

Structura volumului reflectă o progresie logică de la fundamentele geometriei symplectice și planelor lagrangiene către aplicații complexe în mecanica cuantică în spațiul fazelor. Observăm o atenție deosebită acordată indicilor de intersecție, grupului metaplectic și calculului Weyl, elemente esențiale pentru înțelegerea cuantificării. Comparativ cu lucrarea sa Born-Jordan Quantization, unde autorul se concentra pe echivalența tablourilor Schrödinger și Heisenberg, aici perspectiva este mai largă, integrând topologia symplectică în studiul operatorilor de densitate.

Acoperă aceeași arie tematică ca Symplectic Techniques in Physics de Victor Guillemin, dar Symplectic Geometry and Quantum Mechanics se diferențiază printr-o abordare mai tehnică, axată pe teoria operatorilor, servind drept punte către texte avansate de topologie. În timp ce Structure of Dynamical Systems de J.M. Souriau rămâne un text clasic de geometrizare a fizicii, volumul lui de Gosson este mai ancorat în tehnicile moderne de spațiu al fazelor, oferind clarificări necesare asupra unor subiecte precum principiul incertitudinii, tratat aici dintr-o perspectivă geometrică inedită.

Citește tot Restrânge

Din seria Operator Theory: Advances and Applications

  • 18% Operator Theory in Different Settings and Related Applications: 26th IWOTA, Tbilisi, July 2015
    Preț: 90743 lei
  • 18% Square Roots of Elliptic Systems in Locally Uniform Domains
    Preț: 86065 lei
  • 18% Trotter-Kato Product Formulæ
    Preț: 110486 lei
  • 15% Exponentially Dichotomous Operators and Applications
    Preț: 62086 lei
  • 15% Aspects of Boundary Problems in Analysis and Geometry
    Preț: 63531 lei
  • 20% Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory
    Preț: 62079 lei
  • 15% Noncommutative Analysis, Operator Theory and Applications
    Preț: 61791 lei
  • 15% New Trends in the Theory of Hyperbolic Equations
    Preț: 63704 lei
  • 18% Analytic Inequalities and Their Applications in PDEs
    Preț: 108797 lei
  • 15% Approaches to Singular Analysis: A Volume of Advances in Partial Differential Equations
    Preț: 61679 lei
  • 18% Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory: A Volume in Honor of V.E. Katsnelson
    Preț: 97714 lei
  • Parabolicity, Volterra Calculus, and Conical Singularities: A Volume of Advances in Partial Differential Equations
    Preț: 37784 lei
  • Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes: A Collection of Papers Dedicated to Lev Sakhnovich
    Preț: 37951 lei
  • 15% Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators
    Preț: 62086 lei
  • 18% Linear Systems, Signal Processing and Hypercomplex Analysis: Chapman University, November 2017
    Preț: 70265 lei
  • 15% Interpolation, Schur Functions and Moment Problems
    Preț: 62495 lei
  • 15% The State Space Method: Generalizations and Applications
    Preț: 62384 lei
  • 18% Factorization of Matrix and Operator Functions: The State Space Method
    Preț: 92422 lei
  • 18% Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains: Volume I
    Preț: 92057 lei
  • 18% Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II
    Preț: 90947 lei
  • 18% Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
    Preț: 108498 lei
  • 15% Periodic Homogenization of Elliptic Systems
    Preț: 62211 lei
  • 15% Quantization, PDEs, and Geometry: The Interplay of Analysis and Mathematical Physics
    Preț: 61935 lei
  • 15% Generalized Functions and Fourier Analysis: Dedicated to Stevan Pilipović on the Occasion of his 65th Birthday
    Preț: 61791 lei
  • 15% Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations: A Volume of Advances in Partial Differential Equations
    Preț: 62305 lei
  • 15% The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications
    Preț: 56944 lei
  • Spectral Theory of Hyponormal Operators
    Preț: 37284 lei
  • Metric Constrained Interpolation, Commutant Lifting and Systems
    Preț: 39043 lei
  • 15% Parabolic Boundary Value Problems
    Preț: 56239 lei
  • 18% Differential and Integral Operators: International Workshop on Operator Theory and Applications, IWOTA 95, in Regensburg, July 31-August 4, 1995
    Preț: 76211 lei
  • 15% Recent Progress in Operator Theory: International Workshop on Operator Theory and Applications, IWOTA 95, in Regensburg, July 31–August 4,1995
    Preț: 62229 lei
  • Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics: The Carl M. Pearcy Anniversary Volume
    Preț: 36974 lei
  • Chebyshev Splines and Kolmogorov Inequalities
    Preț: 37137 lei
  • Contributions to Operator Theory in Spaces with an Indefinite Metric: The Heinz Langer Anniversary Volume
    Preț: 38433 lei
  • 15% Spectral Theory of Canonical Differential Systems. Method of Operator Identities
    Preț: 61772 lei
  • 15% Mathematical Results in Quantum Mechanics: QMath7 Conference, Prague, June 22–26, 1998
    Preț: 62731 lei
  • The Maz’ya Anniversary Collection: Volume 1: On Maz’ya’s work in functional analysis, partial differential equations and applications
    Preț: 38099 lei

Preț: 108074 lei

Preț vechi: 131798 lei
-18%

Puncte Express: 1621

Carte tipărită la comandă

Livrare economică 04-18 iunie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9783764375744
ISBN-10: 3764375744
Pagini: 392
Ilustrații: XX, 368 p.
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.89 kg
Ediția:2006
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seriile Operator Theory: Advances and Applications, Advances in Partial Differential Equations

Locul publicării:Basel, Switzerland

Public țintă

Research

De ce să citești această carte

Această lucrare este esențială pentru cercetătorii care doresc să stăpânească fundamentele matematice ale cuantificării. Maurice A. de Gosson reușește să clarifice subiecte complexe precum grupurile metaplectice și calculul Weyl, oferind un text de referință care elimină barierele terminologice dintre matematică și fizică. Cititorul câștigă o înțelegere profundă a structurii geometrice din spatele mecanicii cuantice, facilitând accesul către literatura de specialitate de ultimă oră.

Descriere scurtă

Introduction We have been experiencing since the 1970s a process of “symplectization” of S- ence especially since it has been realized that symplectic geometry is the natural language of both classical mechanics in its Hamiltonian formulation, and of its re?nement,quantum mechanics. The purposeof this bookis to providecorema- rial in the symplectic treatment of quantum mechanics, in both its semi-classical and in its “full-blown” operator-theoretical formulation, with a special emphasis on so-called phase-space techniques. It is also intended to be a work of reference for the reading of more advanced texts in the rapidly expanding areas of sympl- tic geometry and topology, where the prerequisites are too often assumed to be “well-known”bythe reader. Thisbookwillthereforebeusefulforbothpurema- ematicians and mathematical physicists. My dearest wish is that the somewhat novel presentation of some well-established topics (for example the uncertainty principle and Schrod ¨ inger’s equation) will perhaps shed some new light on the fascinating subject of quantization and may open new perspectives for future - terdisciplinary research. I have tried to present a balanced account of topics playing a central role in the “symplectization of quantum mechanics” but of course this book in great part represents my own tastes. Some important topics are lacking (or are only alluded to): for instance Kirillov theory, coadjoint orbits, or spectral theory. We will moreover almost exclusively be working in ?at symplectic space: the slight loss in generality is, from my point of view, compensated by the fact that simple things are not hidden behind complicated “intrinsic” notation.

Cuprins

Symplectic Geometry.- Symplectic Spaces and Lagrangian Planes.- The Symplectic Group.- Multi-Oriented Symplectic Geometry.- Intersection Indices in Lag(n) and Sp(n).- Heisenberg Group, Weyl Calculus, and Metaplectic Representation.- Lagrangian Manifolds and Quantization.- Heisenberg Group and Weyl Operators.- The Metaplectic Group.- Quantum Mechanics in Phase Space.- The Uncertainty Principle.- The Density Operator.- A Phase Space Weyl Calculus.

Recenzii

From the reviews:
"De Gosson’s book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Crâsmareanu, Analele Stiintifice
"This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. … This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. … the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e)
“This book covers … symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. … The exposition is very detailed and complete proofs are given. … the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 155 (1), September, 2008)

Textul de pe ultima copertă

This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a  rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices. Thus the keys for the mathematical description of quantum mechanics in phase space are discussed. They are followed by a rigorous geometrical treatment of the uncertainty principle. Then Hilbert-Schmidt and trace-class operators are exposed in order to treat density matrices. In the last chapter the Weyl pseudo-differential calculus is extended to phase space in order to derive a Schrödinger equation in phase space whose solutions are related to those of the usual Schrödinger equation by a wave-packet transform.
The text is essentially self-contained and can be used as basis for graduate courses. Many topics are of genuine interest for pure mathematicians working in geometry and topology.

Caracteristici

Complete theory of the Maslov index and its variants Discussion of the metaplectic group and the Conley-Zehnder index Rigorous mathematical treatment of the Schrödinger equation in phase space Includes supplementary material: sn.pub/extras