Modern Differential Geometry in Gauge Theories PDF Download

Author: Anastasios Mallios
Publisher: Springer Science & Business Media
ISBN: 0817644741
Category : Mathematics
Languages : en
Pages : 303

View

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: Springer Science & Business Media
ISBN: 0817646345
Category : Mathematics
Languages : en
Pages : 244

View

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: M. Göckeler
Publisher: Cambridge University Press
ISBN: 9780521378215
Category : Mathematics
Languages : en
Pages : 248

View

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: Anastasios Mallios
Publisher: Birkhäuser
ISBN: 9780817670900
Category : Mathematics
Languages : en
Pages : 293

View

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: 9780817644765
Category : Mathematics
Languages : en
Pages : 293

View

Book Description

Author: Anastasios Mallios
Publisher:
ISBN:
Category : Gauge fields (Physics)
Languages : en
Pages : 0

View

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: Gregory L. Naber
Publisher: Springer Science & Business Media
ISBN: 1475727429
Category : Mathematics
Languages : en
Pages : 410

View

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: Anastasios Mallios
Publisher:
ISBN:
Category : Gauge fields (Physics)
Languages : en
Pages : 0

View

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: David Bleecker
Publisher: Courier Corporation
ISBN: 0486151875
Category : Science
Languages : en
Pages : 253

View

Book Description
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Author: Loring W. Tu
Publisher: Springer
ISBN: 3319550845
Category : Mathematics
Languages : en
Pages : 347

View

Book Description
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.