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This volume is an introduction to differential methods in physics. Part I contains a comprehensive presentation of the geometry of manifolds and Lie groups, including infinite dimensional settings. The differential geometric notions introduced in Part I are used in Part II to develop selected topics in field theory, from the basic principles up to the present state of the art. This second part is a systematic development of a covariant Hamiltonian formulation of field theory starting from the principle of stationary action.

Geometry, Differential. --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Differential geometry

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Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.

Quantum field theory. --- Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics)

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Extensively classroom-tested, A Course in Field Theory provides material for an introductory course for advanced undergraduateand graduate students in physics. Based on the author’s course that he has been teaching for more than 20 years, the text presents complete and detailed coverage of the core ideas and theories in quantum field theory. It is ideal for particle physics courses as well as a supplementary text for courses on the Standard Model and applied quantum physics.

Field theory (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Cross Sections --- Path Integrals For Fermions --- Quantisation Of Fields --- The Higgs Mechanism --- The Scattering Matrix

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Classical mechanics. Field theory --- Field theory (Physics) --- Least action --- #WNAT:d.d. Prof. L. Bouckaert --- Mechanics --- Variational principles --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Least action. --- Field theory (Physics).

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The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by “standard monomials”. In its modern form, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.

Mathematics. --- Algebraic geometry. --- Algebra. --- Field theory (Physics). --- Algebraic Geometry. --- Field Theory and Polynomials. --- Classical field theory --- Continuum physics --- Algebraic geometry --- Math --- Geometry, algebraic. --- Physics --- Continuum mechanics --- Geometry --- Polynomials. --- Mathematics --- Mathematical analysis