Classical Field Theories
Description
This exceptional textbook provides extensive discussions and worked exercises to accompany a field theory course at the advanced undergraduate or beginning graduate level. There are many questions that arise, both philosophical and practical, during a standard course in classical field theory that are addressed here in discussions between an advanced graduate student and her inquisitive undergrad friend. The discussion involves explicitly working out exercises and making pertinent remarks on the results and potential of the developed formalism. The book is ideal for readers who have taken or are taking the classical field theory course so that they already have a mathematical background in vector and tensor calculus and are willing to learn the basics of differential forms and exterior calculus to gain further insight into field theory formulation. The text can also be used to answer what you've always wanted to know but never dared to ask about field theory.
Reviews / Votes
"The book offers a comprehensive and accessible introduction to the fundamental concepts of classical field theory, covering all the essential aspects required in a formal course. Presented in an innovative and modern format, the content unfolds through a dynamic and engaging conversation between two students, Diego and Aissatou. Diego, a student just beginning his course in classical field theory, faces the complex and profound concepts that this subject entails. Aïssatou, an undoubtedly brilliant young woman, patiently guides him, clearly and precisely explaining the more abstract notions and practical applications of the theory. As their conversation progresses, the reader is led through a pedagogical narrative that eases understanding, offering clear examples and clever analogies that make learning more enjoyable and less intimidating. This work is not only a detailed academic manual but also an intellectual adventure that invites the reader to explore and enjoy the wonderful world of classical field theory." (Ernesto Contreras, University of Alicante, Spain)
"Written with great skill and love, this book deserves to be picked up by anyone who is engaged in or would like to engage in theoretical Physics. That is how, with capital letters, the Authors write about this science. What is unexpected is the style of dialogue they have chosen. Dialogue - explanation through conversation - originates in the European tradition from Socrates and Plato and is realized here in the conversations of two students, Aïssatou and Diego. The surprises don't end there. Unusual, and therefore particularly impressive and pleasant, is the successful design of the text and formulas - at the level of location and font solution, and elegant photos, which reveal the hand and eye of the Author-aesthete, and the discussion of philosophical, historical, and even social aspects of science, which reach the present day. A good selection of material, and detailed explanations, sometimes repeated at different levels, make this book, written with great pedagogical skill, a reliable assistant in travelling through classic field theories!" (Yurij Holovatch, Institute for Condensed Matter Physics, National Academy of Sciences, Lviv, Ukraine)
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Persons
Bertrand Berche is author of about 140 research articles in various fields of physics, mainly statistical physics, condensed matter physics, gauge field theories applied to condensed matter systems, field theories in gravitation and cosmology, but also in complex systems and history of sciences. He taught in various countries, France, Mauritania, Venezuela, Ukraine, Cameroon.
Ernesto Medina is the author of about 120 research articles, mainly in condensed matter physics, but also in statistical mechanics and granular media, and most recently in gauge field theories applied to spin active low dimensional systems. He was a Fulbright Scholar at Arizona State University and is a Fellow of the American Physical Society.
Content
Notation and useful formulas.- Introduction to energy minimization.- Introduction to Lagrangian and Hamiltonian formalisms.- Space-time symmetries, Lie groups, Lie algebras and their representations.- Spacetime symmetries in Minkowski manifold.- Relativistic field theory.- Differential geometry.- Gauge field theory.- A fibre bundle approach to gauge theory.- Curved spacetime field theory.- Alternative relativistic field theories.- Beyond the least action, Path Integral formalism to Quantum Mechanics.