**Author**: Reinhold A. Bertlmann

**Publisher:** Oxford University Press

**ISBN:** 9780198507628

**Category : **Science

**Languages : **en

**Pages : **592

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**Book Description**
This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations

**Author**: Reinhold A. Bertlmann

**Publisher:** Oxford University Press

**ISBN:** 9780198507628

**Category : **Science

**Languages : **en

**Pages : **592

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**Book Description**
This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations

**Author**: Juan Luis Manes

**Publisher:**
**ISBN:**
**Category : **
**Languages : **en

**Pages : **174

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**Book Description**

**Author**: Eduardo Fradkin

**Publisher:** Princeton University Press

**ISBN:** 0691189552

**Category : **Science

**Languages : **en

**Pages : **760

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**Book Description**
The only graduate-level textbook on quantum field theory that fully integrates perspectives from high-energy, condensed-matter, and statistical physics Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has become an invaluable conceptual and mathematical framework for addressing problems across physics, including in condensed-matter and statistical physics. With this expansion of applications has come a new and deeper understanding of quantum field theory—yet this perspective is still rarely reflected in teaching and textbooks on the subject. Developed from a year-long graduate course Eduardo Fradkin has taught for years to students of high-energy, condensed-matter, and statistical physics, this comprehensive textbook provides a fully "multicultural" approach to quantum field theory, covering the full breadth of its applications in one volume. Brings together perspectives from high-energy, condensed-matter, and statistical physics in both the main text and exercises Takes students from basic techniques to the frontiers of physics Pays special attention to the relation between measurements and propagators and the computation of cross sections and response functions Focuses on renormalization and the renormalization group, with an emphasis on fixed points, scale invariance, and their role in quantum field theory and phase transitions Other topics include non-perturbative phenomena, anomalies, and conformal invariance Features numerous examples and extensive problem sets Also serves as an invaluable resource for researchers

**Author**: Bo Summer School Geometric and Topological Methods for Quantum

**Publisher:** American Mathematical Soc.

**ISBN:** 0821840622

**Category : **Mathematics

**Languages : **en

**Pages : **255

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**Book Description**
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

**Author**: Luis Alvarez-Gaumé

**Publisher:** Springer Science & Business Media

**ISBN:** 3642237274

**Category : **Science

**Languages : **en

**Pages : **299

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**Book Description**
This book provides an introduction to Quantum Field Theory (QFT) at an elementary level—with only special relativity, electromagnetism and quantum mechanics as prerequisites. For this fresh approach to teaching QFT, based on numerous lectures and courses given by the authors, a representative sample of topics has been selected containing some of the more innovative, challenging or subtle concepts. They are presented with a minimum of technical details, the discussion of the main ideas being more important than the presentation of the typically very technical mathematical details necessary to obtain the final results. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework.

**Author**: Peter Van

**Publisher:** Cornell University Press

**ISBN:**
**Category : **Science

**Languages : **en

**Pages : **120

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**Book Description**
The conditions of Alvarez-Gaume and Witten for transversality of Feynman diagrams with loops of chiral spin 1/2, schiral spin 3/2 or selfdual antisymmetric tensors, coupled to external gravitons and Yang-Mills bosons, are dirived. The resuls are then applied to the N=1 and N=2B supergravities in d=10 dimensions. For the N=2B theory, all gravitational anomalies cancel by themselves, but for the N=1 theory, counterterms are constructed, using the descent equations, which cancel the anomalies. The latter result, due to Green and Schwarz, triggered the recent interest in string theories. These lectures are selfcontained and detailed, at the level of a graduate course in particle physics. The content is based on lectures given by the author at the K.U.Leuven in January 1989.

**Author**: Eike Bick

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540231257

**Category : **Mathematics

**Languages : **en

**Pages : **380

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**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, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

**Author**: Robert Eugene Marshak

**Publisher:** World Scientific

**ISBN:** 9789810211066

**Category : **Science

**Languages : **en

**Pages : **708

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**Book Description**
For scientific, technological and organizational reasons, the end of World War II (in 1945) saw a rapid acceleration in the tempo of discovery and understanding in nuclear physics, cosmic rays and quantum field theory, which together triggered the birth of modern particle physics. The first fifteen years (1945-60) following the war's end ? the ?Startup Period? in modern particle physics -witnessed a series of major experimental and theoretical developments that began to define the conceptual contours (non-Abelian internal symmetries, Yang-Mills fields, renormalization group, chirality invariance, baryon-lepton symmetry in weak interactions, spontaneous symmetry breaking) of the quantum field theory of three of the basic interactions in nature (electromagnetic, strong and weak). But it took another fifteen years (1960-75) ? the ?Heroic Period? in modern particle physics ? to unravel the physical content and complete the mathematical formulation of the standard gauge theory of the strong and electroweak interactions among the three generations of quarks and leptons. The impressive accomplishments during the ?Heroic Period? were followed by what is called the ?period of consolidation and speculation (1975-1990)?, which includes the experimental consolidation of the standard model (SM) through precision tests, theoretical consolidation of SM through the search for more rigorous mathematical solutions to the Yang-Mills-Higgs equations, and speculative theoretical excursions ?beyond SM?.Within this historical-conceptual framework, the author ? himself a practicing particle theorist for the past fifty years ? attempts to trace the highlights in the conceptual evolution of modern particle physics from its early beginnings until the present time. Apart from the first chapter ? which sketches a broad overview of the entire field ? the remaining nine chapters of the book offer detailed discussions of the major concepts and principles that prevailed and were given wide currency during each of the fifteen-year periods that comprise the history of modern particle physics. Those concepts and principles that contributed only peripherally to the standard model are given less coverage but an attempt is made to inform the reader about such contributions (which may turn out to be significant at a future time) and to suggest references that supply more information. Chapters 2 and 3 of the book cover a range of topics that received dedicated attention during the ?Startup Period? although some of the results were not incorporated into the structure of the standard model. Chapters 4-6 constitute the core of the book and try to recapture much of the conceptual excitement of the ?Heroic Period?, when quantum flavordynamics (QFD) and quantum chromodynamics (QCD) received their definitive formulation. [It should be emphasized that, throughout the book, logical coherence takes precedence over historical chronology (e.g. some of the precision tests of QFD are discussed in Chapter 6)]. Chapter 7 provides a fairly complete discussion of the chiral gauge anomalies in four dimensions with special application to the standard model (although the larger unification models are also considered). The remaining three chapters of the book (Chapters 7-10) cover concepts and principles that originated primarily during the ?Period of Consolidation and Speculation? but, again, this is not a literal statement. Chapters 8 and 9 report on two of the main directions that were pursued to overcome acknowledged deficiencies of the standard model: unification models in Chapter 8 and attempts to account for the existence of precisely three generations of quarks and leptons, primarily by means of preon models, in Chapter 9. The most innovative of the final three chapters of the book is Chapter 10 on topological conservation laws. This last chapter tries to explain the significance of topologically non-trivial solutions in four-dimensional (space-time) particle physics (e.g. 't Hooft-Polyakov monopoles, instantons, sphalerons, global SU(2) anomaly, Wess-Zumino term, etc.) and to reflect on some of the problems that have ensued (e.g. the ?strong CP problem? in QCD) from this effort. It turns out that the more felicitous topological applications of field theory are found ? as of now ? in condensed matter physics; these successful physical applications (to polyacetylene, quantized magnetic flux in type-II low temperature superconductivity, etc.) are discussed in Chapter 10, as a good illustration of the conceptual unity of modern physics.

**Author**: Gerhard Grensing

**Publisher:** World Scientific

**ISBN:** 9811237093

**Category : **Science

**Languages : **en

**Pages : **1656

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**Book Description**
The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.

**Author**: Tian Yu Cao

**Publisher:** Cambridge University Press

**ISBN:** 9780521602723

**Category : **Science

**Languages : **en

**Pages : **424

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**Book Description**
Multi-author volume on the history and philosophy of physics.