Geometry, Topology and Quantization (Mathematics and Its Applications)

Book Description

This monograph deals with the geometrical and topological aspects associated with the quantization procedure, and it is shown how these features are manifested in anomaly and Berry Phase. This book is unique in its emphasis on the topological aspects of a fermion which arise as a consequence of the quantization procedure. Also, an overview of quantization procedures is presented, tracing the equivalence of these methods by noting that the gauge field plays a significant role in all these procedures, as it contains the ingredients of topological features.
Audience: This book will be of value to research workers and specialists in mathematical physics, quantum mechanics, quantum field theory, particle physics and differential geometry.

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Beyond Conventional Quantization
John R. Klauder
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521675480

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This text describes novel treatments of quantum problems using enhanced quantization procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory. Beginning with a review of classical mechanics, the book goes on to detail Hilbert space, quantum mechanics, and scalar quantum field theory. Later chapters further develop analytical skills, study a special class of models, and present a discussion of continuous and discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Throughout, symmetry is used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included.

Quantum Geometry: A Statistical Field Theory Approach (Cambridge Monographs on Mathematical Physics)

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Quantum Geometry: A Statistical Field Theory Approach (Cambridge Monographs on Mathematical Physics)
Jan Ambjørn , Bergfinnur Durhuus , and Thordur Jonsson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 052101736X

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This graduate level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantization of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two-and higher-dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.

Topology and Geometry in Physics (Lecture Notes in Physics)

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Topology and Geometry in Physics (Lecture Notes in Physics)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540231250

Book Description

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Quantum Field Theory and Noncommutative Geometry (Lecture Notes in Physics)

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Quantum Field Theory and Noncommutative Geometry (Lecture Notes in Physics)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540239006

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This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.

Maslov Classes, Metaplectic Representation and Lagrangian Quantization (Mathematical Research Vol. 5)

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Maslov Classes, Metaplectic Representation and Lagrangian Quantization (Mathematical Research Vol. 5)
Maurice de Gosson
Manufacturer: Wiley-VCH
ProductGroup: Book
Binding: Paperback

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ASIN: 3527400877

Book Description

The Maslov Classes have been playing an essential role in various parts of applied and pure mathematics, and physics, since the early 70's. Their correct definition is due to V. I. Arnold and J. Leray, in the transversal case, and to P. Dazord and the author in the general case. The aim of this book is to give a thorough treatment of the theory of the Maslov classes and of their relationship with the metaplectic group. It is (among other things) shown that these classes can be reconstructed, modulo 4, using only the analytic properties of the metaplectic group. In the last chapter the author sketches a scheme for geometric quantization by introducing two new concepts, that of metaplectic half-form and that of Lagrangian catalogue, the latter generalizes and simplifies the notion of "Lagrangian function" introduced by J. Leray. A Lagrangian catalogue is a collection of metaplectic half-forms which are themselves "cohomological wave functions", whose definition is made possible by using the combinatorial properties of the Maslov classes. The transformation of Lagrangian catalogues under the metaplectic group and of Hamiltonian flows is studied, and it is shown that one thus recovers very easily the so-called "quasi-classical approximation" to the solutions of Schrödinger equation if one introduces a natural concept, that of projection of a Lagrangian catalogue. An application to geometric phase shifts, including Berry's phase, is given.

Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete: Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable ... II: Mathematics, Physics and Chemistry)

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Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete: Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable ... II: Mathematics, Physics and Chemistry)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Coherent Transform, Quantization, & Poisson Geometry (American Mathematical Society Translations Series 2)

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Coherent Transform, Quantization, & Poisson Geometry (American Mathematical Society Translations Series 2)

Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Hardcover

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Book Description

This volume contains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.

Completely Prime Maximal Ideals and Quantization (Memoirs of the American Mathematical Society)

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Completely Prime Maximal Ideals and Quantization (Memoirs of the American Mathematical Society)
William M. McGovern
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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This monograph will appeal to graduate students and researchers interested in Lie algebras. McGovern classifies the completely prime maximal spectrum of the enveloping algebra of any classical semisimple Lie algebra. He also studies finite algebra extensions of completely prime primitive quotients of such enveloping algebras and computes their lengths as bimodules, characteristic cycles, and Goldie ranks in many cases. This work marks a major advance in the quantization program, which seeks to extend the methods of (commutative) algebraic geometry to the setting of enveloping algebras. While such an extension cannot be completely carried out, this work shows that many partial results are available.

Conférence Moshé Flato 1999: Quantization, Deformations, and Symmetries Volume I (Mathematical Physics Studies)

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Conférence Moshé Flato 1999: Quantization, Deformations, and Symmetries Volume I (Mathematical Physics Studies)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792365402

Book Description

These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity.
With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena.
Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.

Book Description

The novel is the story of Dreyer, a wealthy and boisterous proprietor of a men's clothing emporium store. Ruddy, self-satisfied, and thoroughly masculine, he is perfectly repugnant to his exquisite but cold middle-class wife Martha. Attracted to his money but repelled by his oblivious passion, she longs for their nephew instead, the myopic Franz. Newly arrived in Berlin, Franz soon repays his uncle's condescension in his aunt's bed.

Customer Reviews:

Well, well, well..........2006-03-24

It has taken me a long time, but I have finally found what I consider to be a mediocre piece of writing by Nabokov. Apparently he partially wrote it languidly sprawled on a beach sometime during an idle period in his late twenties, and it shows. It is a bright piece of fiction, but lazily put together. The characters do not sparkle, the love traingle plot is tiresome, and even the style seems somewhat deadened - there are some highlights, such as country boy Franz blundering myopically through Berlin without his glasses - but too much of this novel attempts whimsical virtuousity but ends up coming across as sterile. Witness the terrible innuendos to describe orgasms - you can spot them...

Nabokov's Second.......2004-07-11

Nabokov's second novel, his brightest and lightest of the lot, is regarded by some as being one of the weaker links in the author's ouvre.The plot here is pretty banal (a bland, country boy Franz falls in love with the wife of his rich uncle who lives in Berlin and before you know it Franz and his aunt are pathetically planning the murder of the middle-man). Nabokov pokes some fun at the story of Madame Bovary and offers somewhat of a parody. As usual though, the plot here takes backstage to the form and style of writing and Nabokov does not disappoint; the prose is beautiful and enchanting (minus some laughable sexual innuendos and so on) and makes the novel worth reading.While it's far from counting among Nabokov's strongest works, I still enjoyed the book and certain images have and will remain with me (especially the last couple of chapters, filled with the imagery of azure beaches and wide open skies). Nabokov does make an 'appearance' in the novel (a la Hitchcock), along with his wife, as the couple with whom Franz becomes somewhat obsessed at the seaside resort (look for mention of the butterfly net).This is a relatively light and accessible Nabokov read, recommended for shiny summer days.

Not Lolita, by any means, but still a good read.......2004-07-02

Franz has come to Berlin for a job. His mother's wealthy cousin (Dreyer) has kindly agreed to take him on in his department store. What neither Dreyer nor Franz has considered is that Mrs. Martha Dreyer would also kindly consent to take him on as her lover. It takes a little planning on her part, but finally the shy, lanky Franz becomes her secret lover, her ticket to a world without Dreyer.

King, Queen, Knave is a typical triangle love story. And yet, it's not. Nabokov, even in this early novel, has an excellent feel for human beings, what makes them do what they do and just how much they can stand. Franz and Martha's relationship moves from the sublime to the detestable for Franz, while he becomes a lifeline to Martha. Dreyer, seeing good in all the world, is easily duped--though easily duping Martha on the side.

As with Lolita, the plot is not all that great, and I can't truly say I "enjoyed" the book. But nonetheless, I couldn't stop reading it. I had to continue watching the dynamics change between the King, the Queen and the Knave and see just how the hand was played out.

a mere preview.......2004-05-01

the attraction of this book is the sense of things to come with regards to the author's future books. whereas "mary", nabokov's first novel, emits a warm autobiographic glow, "king, queen, knave" does an about face to depict a world utterly distant and alien from the author's personal milieux. the result is an abstract world not quite as pure and fantastic as the one created in "lolita", indeed the former pales greatly by comparison, but an abstract world which is nonetheless plausible and artistically pleasing. there are two unforgettable images in this novel. one adumbrates nabokov's penchant for condemning cruelty by having his characters indulge in it, that very cruelty, with inexcusable zest and relish; while the other gives us a taste of the author's wicked sense of humor. they are: marthe's repeated beatings and/or chastisements of tom, the family dog, and the pathetic fate of the monkey, a gift for marthe from dreyer before their marriage, which burns itself trying to light a match. these two images, which are patented nabokov, are just the tip of the iceberg in a body of work abrim with unforgettable images.

A Poetic, funny, erotic entertainment.......2002-08-17

Vladmir Nabakov may be the closest kin in the twentieth century to the magnificent imagination of "The one thousand and one Arabian Nights". Yet this is not entirely an apt comparison, for whereas the "Nights" was a framework in which the dreams were presented as a reality, Nabakov's is a strange world wherein the reality is painted as a lush, evanescent dream. But beware the reader, who thinks this mere clever wordplay, for to read Nabakov is to be entranced into a highly sophisticated web where life is as much a romantic dirge as a brilliant puzzle. King, Queen, Knave was by his own admission, "my gayest novel", and yet there is a kind of sadness here amidst the gaiety and superlative sequence of almost divine juxtapositions that I have only experienced from the likes of a virtuoso rendition of Paganini.
The basic story is a simple love triangle, a rich Uncle, a faux nephew and a cold aunt, and of course involves an illicit affair culminating in a murderous plot. And yet what is not simple is how Nabakov deftly draws these characters, at once ultra real and but also aloof, blatant caricatures of the human soul. Like a pack of playing cards, thinking themselves to be free, but fully boxed in. And it's quite amusingly funny, but Nabakov's humor springs from diverse and often mundane sources - the ambience, the shaggy dog, the inward blindness of his protagonists and situations involving the Uncle and the two lovers where the former is completely unaware that he is being cuckolded right under his canopy. Personally, though, what I find most delightful is the poetic details that N throws in gratuitously everywhere, e.g.- The time when Uncle Dreyer, who is the owner of a large Berlin Department store pays a surprise visit to his nephew and his cohorts who work in the sporting goods dept. And "An early customer, who wanted another ball for his dog, was ignored for an instant" or consider "an old sculptor whose work was so lifelike that he managed to convey the impression of acute chorea". The descriptions of the lovemaking are also highly erotic - but I won't quote from that, not to mention the brilliant morphing of scenes and persons. Enough said. This book is a veritable masterpiece and a highly entertaining one at that.
One final quote: "A baker in the encyclopedia who had poisoned an entire parish told the prison barber who was shaving his neck that never in his life had he slept so well".
And there is a wonderful twist even in the last paragraph.

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KING, QUEEN, KNAVE

Manufacturer: Fawcett
ProductGroup: Book
Binding: Mass Market Paperback

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King Queen Knave 1ST Edition
Vladimir Nabokov
Manufacturer: MCGRAW HILL PUBLISHING COMPANY
ProductGroup: Book
Binding: Hardcover

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King, Queen, Knave

Manufacturer: McGraw Hill
ProductGroup: Book
Binding: Hardcover

Product Description

Novel written by Vladimir Nabokov, published in 1968, First Edition, Second Printing. Cloth bound in black. Gold Imprint on back 45715, edition number.

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King, Queen, Knave
Vladimir Nabokov
Manufacturer: Fawcett Crest
ProductGroup: Book
Binding: Mass Market Paperback

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King, Queen, Knave

Manufacturer: McGraw Hill, Inc.
ProductGroup: Book
Binding: Hardcover

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King, Queen, Knave
Vladimir Nabokov
Manufacturer: McGraw-Hill Companies
ProductGroup: Book
Binding: Paperback

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King, Queen, Knave
Vladimir Nabokov
Manufacturer: MCGRAW-HILL BOOK COMPANY
ProductGroup: Book
Binding: Hardcover

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King, Queen, Knave
Vladimir Nabokov
Manufacturer: Penguin
ProductGroup: Book
Binding: Paperback

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King, Queen, Knave
Vladimir Nabokov
Manufacturer: McGraw-Hill Book Company
ProductGroup: Book
Binding: Hardcover

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