This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Priscila de Aquino Название: Beyond Standard Model Phenomenology at the LHC ISBN: 3319376462 ISBN-13(EAN): 9783319376462 Издательство: Springer Рейтинг: Цена: 13059.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides an introduction to the physics of the Standard Model and beyond, and to the methods used to analyze Large Hadron Collider data. It presents a full phenomenological search for graviton emission in a multi-jet final state.
Автор: Vergados Ioannis John Demetrius Название: Standard Model And Beyond, The ISBN: 9813275774 ISBN-13(EAN): 9789813275775 Издательство: World Scientific Publishing Рейтинг: Цена: 7920.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book contains a systematic and pedagogical exposition of recent developments in particle physics and cosmology. It starts with two introductory chapters on group theory and the Dirac theory. Then it proceeds with the formulation of the Standard Model (SM) of Particle Physics, particle content and symmetries, fully exploiting the material of the first two chapters. It discusses the concept of gauge symmetries and emphasizes their role in particle physics. It then analyses the Higgs mechanism and the spontaneous symmetry breaking (SSB). It explains how the particles (gauge bosons and fermions) after the SSB acquire a mass and get admixed. The various forms of the charged currents are discussed in detail as well as how the parameters of the SM, which cannot be determined by the theory, are fixed by experiment, including the recent LHC data and the Higgs discovery. Quantum chromodynamics is discussed and various low energy approximations to it are presented. The Feynman diagrams are introduced and applied, at the level of first year graduate students.
Examples are the evaluation of the decay widths of the gauge bosons and some cross sections for interesting processes such as Rutherford scattering, electron-proton scattering (elementary proton or described by a form factor, and inelastic scattering) and Compton scattering.
After that the classic topics like the role of C, P, CP symmetries and the experimental methods needed to verify their conservation or violation are discussed in some detail. Topics beyond the standard model, like supersymmetry for pedestrians and grand unification, are discussed.
To this end neutrino oscillations, dark matter and baryon asymmetry are also briefly discussed at the first year graduate level. Finally, the book contains an exhibition of recent developments in cosmology, especially from the elementary particle point of view.
Автор: Priscila de Aquino Название: Beyond Standard Model Phenomenology at the LHC ISBN: 3319007610 ISBN-13(EAN): 9783319007618 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides an introduction to the physics of the Standard Model and beyond, and to the methods used to analyze Large Hadron Collider data. It presents a full phenomenological search for graviton emission in a multi-jet final state.
Автор: Vergados Ioannis John Demetrius Название: Standard Model And Beyond, The ISBN: 9813228555 ISBN-13(EAN): 9789813228559 Издательство: World Scientific Publishing Рейтинг: Цена: 13622.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains a systematic and pedagogical exposition of recent developments in particle physics and cosmology. It starts with two introductory chapters on group theory and the Dirac theory.
Автор: Ghosh Saranya Samik, Hebbeker Thomas, Meyer Arnd Название: General Model Independent Searches for Physics Beyond the Standard Model ISBN: 303053782X ISBN-13(EAN): 9783030537821 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This primer describes the general model independent searches for new physics phenomena beyond the Standard Model of particle physics.
Описание: This book offers a self-contained introduction to the theory of electroweak interactions based on the semi-classical approach to relativistic quantum field theory, with thorough discussion of key aspects of the field.
Автор: Langacker Название: The Standard Model & Beyond, 2Nd Ed ISBN: 1498763219 ISBN-13(EAN): 9781498763219 Издательство: Taylor&Francis Рейтинг: Цена: 6600.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This new edition of The Standard Model and Beyond presents an advanced introduction to the physics and formalism of the standard model and other non-abelian gauge theories. It provides a solid background for understanding supersymmetry, string theory, extra dimensions, dynamical symmetry breaking, and cosmology. In addition to updating all of the experimental and phenomenological results from the first edition, it contains a new chapter on collider physics; expanded discussions of Higgs, neutrino, and dark matter physics; and many new problems.
The book first reviews calculational techniques in field theory and the status of quantum electrodynamics. It then focuses on global and local symmetries and the construction of non-abelian gauge theories. The structure and tests of quantum chromodynamics, collider physics, the electroweak interactions and theory, and the physics of neutrino mass and mixing are thoroughly explored. The final chapter discusses the motivations for extending the standard model and examines supersymmetry, extended gauge groups, and grand unification.
Thoroughly covering gauge field theories, symmetries, and topics beyond the standard model, this text equips readers with the tools to understand the structure and phenomenological consequences of the standard model, to construct extensions, and to perform calculations at tree level. It establishes the necessary background for readers to carry out more advanced research in particle physics.
Supplementary materials are provided on the author's website and a solutions manual is available for qualifying instructors.
Описание: This book offers a self-contained introduction to the theory of electroweak interactions based on the semi-classical approach to relativistic quantum field theory, with thorough discussion of key aspects of the field.
Автор: Nair, V. Parameswaran (city College Of New York, Usa) Название: Concepts in particle physics: a concise introduction to the standard model ISBN: 9813227559 ISBN-13(EAN): 9789813227552 Издательство: World Scientific Publishing Рейтинг: Цена: 13622.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The 2013 discovery of the Higgs boson posed a challenge to both physics undergraduates and their instructors. Since particle physics is seldom taught at the undergraduate level, the question 'what is the Higgs and why does its discovery matter?' is a common question among undergraduates. Equally, answering this question is a problem for physics instructors.This book is an attempt to put the key concepts of particle physics together in an appealing way, and yet give enough extra tidbits for students seriously considering graduate studies in particle physics. It starts with some recapitulation of relativity and quantum mechanics, and then builds on it to give both conceptual ideas regarding the Standard Model of particle physics as well as technical details. It is presented in an informal lecture style, and includes 'remarks' sections where extra material, history, or technical details are presented for the interested student. The last lecture presents an assessment of the open questions, and where the future might take us.
This book takes the reader from some elementary ideas about groups to the essence of the Standard Model of particle physics along a relatively straight and intuitive path. Groups alone are first used to arrive at a classical analog of the Dirac equation. Using elementary quantum mechanics, this analog can be turned into the actual Dirac equation, which governs the motion of the quarks and leptons of the Standard Model. After an introduction to the gauge principle, the groups introduced in the beginning of the book are used to give an introduction to the Standard Model. The idea is to give an Olympian view of this evolution, one that is often missing when absorbing the detailed subject matter of the Standard Model as presented in an historical approach to the subject.
Sample Chapter(s)
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