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Author: Albert S. Schwarz Publisher: Springer Science & Business Media ISBN: 366202943X Category : Mathematics Languages : en Pages : 277
Book Description
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
Author: Albert S. Schwarz Publisher: Springer Science & Business Media ISBN: 366202943X Category : Mathematics Languages : en Pages : 277
Book Description
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
Author: T R Govindarajan Publisher: World Scientific ISBN: 9811270449 Category : Science Languages : en Pages : 340
Book Description
A P Balachandran has a long and impressive record of research in particle physics and quantum field theory, bringing concepts of geometry, topology and operator algebras to the analysis of physical problems, particularly in particle physics and condensed matter physics. He has also had an influential role within the physics community, not only in terms of a large number of students, research associates and collaborators, but also serving on the editorial boards of important publications, including the International Journal of Modern Physics A.This book consists of articles by students and associates of Balachandran. Most of the articles are scientific in nature, with topics ranging from noncommutative geometry, particle physics phenomenology, to condensed matter physics. Various chapters focus on new perspectives and directions resulting from Balachandran's contributions to physics, as well as some reminiscences of collaborating and working with Balachandran.
Author: Daniel S. Freed Publisher: American Mathematical Soc. ISBN: 1470452065 Category : Mathematics Languages : en Pages : 202
Book Description
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Author: Brian Hatfield Publisher: CRC Press ISBN: 0429972865 Category : Science Languages : en Pages : 474
Book Description
First Published in 2018. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory
Author: Xiao-Gang Wen Publisher: OUP Oxford ISBN: 0191523968 Category : Science Languages : en Pages : 520
Book Description
For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.
Author: Alexander Altland Publisher: Cambridge University Press ISBN: 0521769752 Category : Science Languages : en Pages : 785
Book Description
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Author: Gregory Naber Publisher: Springer Science & Business Media ISBN: 9780387949468 Category : Mathematics Languages : en Pages : 428
Book Description
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Author: Rodney A Brooks Publisher: Independently Published ISBN: Category : Languages : en Pages : 0
Book Description
Fields of Color explains Quantum Field Theory to a lay audience without equations. It shows how this often overlooked theory resolves the weirdness of Quantum Mechanics and the paradoxes of Relativity. The third edition contains a new solution to the measurement problem ("the most controversial problem in physics today") and shows the quantum basis for Einstein's famous E = mc2.
Author: Gregory L. Naber Publisher: Springer Science & Business Media ISBN: 1475727429 Category : Mathematics Languages : en Pages : 410
Book Description
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Author: Albert S. Schwarz
Author: Albert S. Schwarz
Author: T R Govindarajan
Author: Daniel S. Freed
Author: Brian Hatfield
Author: Xiao-Gang Wen
Author: Alexander Altland
Author: Gregory Naber
Author: Rodney A Brooks
Author: Gregory L. Naber
Author: Billy McCormac