Classical Field Theories A Student Companion

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.

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.

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.