scholarly journals Differential Geometry in Physics

2021 ◽  
Author(s):  
Gabriel Lugo
Keyword(s):  
Differential Geometry ◽  
Applied Mathematics ◽  
Optimal Path ◽  
Theoretical Physics ◽  
Doctoral Degrees ◽  
Dirac Monopole ◽  
Modern Approach ◽  
Curves And Surfaces ◽  
Master's Thesis ◽  
Mathematical Foundations

Differential Geometry in Physics is a treatment of the mathematical foundations of the theory of general relativity and gauge theory of quantum fields. The material is intended to help bridge the gap that often exists between theoretical physics and applied mathematics. The approach is to carve an optimal path to learning this challenging field by appealing to the much more accessible theory of curves and surfaces. The transition from classical differential geometry as developed by Gauss, Riemann and other giants, to the modern approach, is facilitated by a very intuitive approach that sacrifices some mathematical rigor for the sake of understanding the physics. The book features numerous examples of beautiful curves and surfaces often reflected in nature, plus more advanced computations of trajectory of particles in black holes. Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons. Features of this book: * Chapters 1-4 and chapter 5 comprise the content of a one-semester course taught by the author for many years. * The material in the other chapters has served as the foundation for many master’s thesis at University of North Carolina Wilmington for students seeking doctoral degrees. * An open access ebook edition is available at Open UNC (https://openunc.org) * The book contains over 80 illustrations, including a large array of surfaces related to the theory of soliton waves that does not commonly appear in standard mathematical texts on differential geometry.

scholarly journals GEORGE KEITH BATCHELOR 8 March 1920–30 March 2000 Founding Editor, Journal of Fluid Mechanics, 1956

2000 ◽  
Vol 421 ◽  
pp. 1-14 ◽  
Author(s):  
HERBERT E. HUPPERT
Keyword(s):  
Fluid Mechanics ◽  
International Organizations ◽  
Solid Mechanics ◽  
Applied Mathematics ◽  
Fluid Flows ◽  
Theoretical Physics ◽  
Founding Editor ◽  
Number Of Factors ◽  
Quantitative Understanding ◽  
The Subject

George Batchelor was one of the giants of fluid mechanics in the second half of the twentieth century. He had a passion for physical and quantitative understanding of fluid flows and a single-minded determination that fluid mechanics should be pursued as a subject in its own right. He once wrote that he ‘spent a lifetime happily within its boundaries’. Six feet tall, thin and youthful in appearance, George's unchanging attire and demeanour contrasted with his ever-evolving scientific insights and contributions. His strongly held and carefully articulated opinions, coupled with his forthright objectivity, shone through everything he undertook.George's pervasive influence sprang from a number of factors. First, he conducted imaginative, ground-breaking research, which was always based on clear physical thinking. Second, he founded a school of fluid mechanics, inspired by his mentor G. I. Taylor, that became part of the world renowned Department of Applied Mathematics and Theoretical Physics (DAMTP) of which he was the Head from its inception in 1959 until he retired from his Professorship in 1983. Third, he established this Journal in 1956 and actively oversaw all its activities for more than forty years, until he relinquished his editorship at the end of 1998. Fourth, he wrote the monumental textbook An Introduction to Fluid Dynamics, which first appeared in 1967, has been translated into four languages and has been relaunched this year, the year of his death. This book, which describes the fundamentals of the subject and discusses many applications, has been closely studied and frequently cited by generations of students and research workers. It has already sold over 45 000 copies. And fifth, but not finally, he helped initiate a number of international organizations (often European), such as the European Mechanics Committee (now Society) and the biennial Polish Fluid Mechanics Meetings, and contributed extensively to the running of IUTAM, the International Union of Theoretical and Applied Mechanics. The aim of all of these associations is to foster fluid (and to some extent solid) mechanics and to encourage the development of the subject.

Differential Geometry of Curves and Surfaces with Singularities

10.1142/12284 ◽  
2021 ◽  
Author(s):  
Masaaki Umehara ◽  
Kentaro Saji ◽  
Kotaro Yamada ◽  
Wayne Rossman
Keyword(s):  
Differential Geometry ◽  
Curves And Surfaces

scholarly journals Asymptotology—a cautionary tale

2002 ◽  
Vol 44 (1) ◽  
pp. 33-40 ◽  
Author(s):  
R. L. Dewar
Keyword(s):  
Eigenvalue Problem ◽  
Applied Mathematics ◽  
Theoretical Physics ◽  
Local Analysis ◽  
Cautionary Tale ◽  
Stokes Phenomenon ◽  
Solvable Problem ◽  
Exactly Solvable ◽  
Continuous Range

AbstractThe art of asymptotology is a powerful tool in applied mathematics and theoretical physics, but can lead to erroneous conclusions if misapplied. A seemingly paradoxical case is presented in which a local analysis of an exactly solvable problem appears to find solutions to an eigenvalue problem over a continuous range of the eigenvalue, whereas the spectrum is known to be discrete. The resolution of the paradox involves the Stokes phenomenon. The example illustrates two of Kruskal's Principles of Asymptotology.

scholarly journals Editorial

2014 ◽  
Vol 60 ◽  
pp. 1-4
Author(s):  
Trevor Stuart
Keyword(s):  
Differential Geometry ◽  
London Mathematical Society ◽  
Theoretical Physics ◽  
Chern Classes ◽  
Common Currency ◽  
Medical Sciences ◽  
The Usa ◽  
History Of ◽  
Obituary Notice ◽  
Bonnet Theorem

As is usual, the volumes of Biographical Memoirs contain much material of interest to the student of the mathematical, physical, engineering, biological and medical sciences. Often a memoir has been written in collaboration with another Academy or Society. In the present volume the memoir of Shiing-Shen Chern is an expanded version of an obituary notice by Nigel Hitchin that appeared in the Bulletin of the London Mathematical Society . Chern was a great geometer, who revolutionized differential geometry and whose mathematical tools are now common currency in geometry, topology and theoretical physics. His proof of the Gauss–Bonnet theorem, which was a pivotal event in the history of differential geometry, led to the importance of the Chern classes. Moreover. S.-S. Chern was extremely influential in the development of mathematics and geometry both in the USA, at the Institute of Advanced Study, Princeton, and Chicago and Berkeley, and in China, in Shanghai and Nankei.

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

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