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Author: Anastasios Mallios Publisher: Springer Science & Business Media ISBN: 0817646345 Category : Mathematics Languages : en Pages : 244
Book Description
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author: Anastasios Mallios Publisher: Springer Science & Business Media ISBN: 0817646345 Category : Mathematics Languages : en Pages : 244
Book Description
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author: Anastasios Mallios Publisher: ISBN: Category : Gauge fields (Physics) Languages : en Pages : 0
Book Description
Presenting a modern differential geometry approach to physical theories, such as the Gauge theory, Sheaf theory (geometry) and sheaf cohomology (analysis) are used to explain the machinery of classical differential geometry. There is also discussion of the applications of differential geometry to physical theories.
Author: Anastasios Mallios Publisher: Springer Science & Business Media ISBN: 0817644741 Category : Mathematics Languages : en Pages : 303
Book Description
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author: Anastasios Mallios Publisher: Birkhäuser ISBN: 9780817670900 Category : Mathematics Languages : en Pages : 293
Book Description
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author: M. Göckeler Publisher: Cambridge University Press ISBN: 9780521378215 Category : Mathematics Languages : en Pages : 248
Book Description
Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.
Author: C J Isham Publisher: World Scientific ISBN: 9814507288 Category : Languages : en Pages : 192
Book Description
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course “Fundamental Fields and Forces” at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, non-linear sigma-models and other types of non-linear field systems that feature in modern quantum field theory. This volume is in three parts dealing with, respectively, (i) introductory coordinate-free differential geometry, (ii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, (iii) introduction to the theory of fibre bundles. In the first part of the book the author has laid considerable stress on the basic ideas of “tangent space structure” which he develops from several different points of view: some geometrical, and others more algebraic. This is done with the awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry. Contents:An Introduction to TopologyDifferentiable ManifoldsVector Fields and n-FormsLie GroupsFibre BundlesConnections in a Bundle
Author: Michael F. Atiyah Publisher: Edizioni della Normale ISBN: Category : Mathematics Languages : en Pages : 110
Book Description
These Lecture Notes are an expanded version of the Fermi Lectures I gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978. In all cases I was addressing a mixed audience of mathematicians and physicists and the presentation had to be tailored accordingly. Throughout, I presented the mathematical material in a somewhat unorthodox order, following a pattern which I felt would relate the new techniques to familiar ground for physicists. The main new results presented in the lectures, namely the construction of all multi-istanton solutions of Yang-Mills fields, is the culmination of several years of fruitful interaction between many physicists and mathematicians. The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his “twistor programme” were ideally suited to the study of the Yang-Mills equations. The instanton problem was then seen to be equivalent to a problem in complex analysis and to one in algebraic geometry. Using the powerful methods of modern algebraic geometry it was not long before the problem was finally solved.
Author: Lance Bailey Publisher: Nova Science Publishers ISBN: 9781634835466 Category : Gauge fields (Physics) Languages : en Pages : 0
Book Description
This book revisits the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups. The gauge theory of gravity is also established, in which spinorial and ventorial matter fields serve as gravitating sources. The potential applications of the present gauge theory of gravity, including quantum-vacuum-energy gravity, cosmological constant problem and gravity-gauge unification is also addressed. The third chapter focuses on a gravitational gauge theory with spin connection and vierbein as fundamental variables of gravity. Next, the place and physical significance of Poincaré gauge theory of gravity (PGTG) in the framework of gauge approach to gravitation is discussed. A cutoff regularization method in gauge theory is discussed in Chapter Five. The remaining chapters in the book focus on differential geometry, in particular, the authors show how fractional differential derived from fractional difference provides a basis to expand a theory of fractional differential geometry which would apply to non-differentiable manifolds; a review of the infinitesimal Baker-Campbell-Hausdorff formula is provided and the book concludes with a short communication where the authors focus on local stability, and describe how this leads naturally into the question of finite-time singularities and generalized soliton solutions.
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.