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Including didactic introductions to the main topics in the theory of fields, this text gives students of the subject concise explanations of the fundamentals essential for applying the theory as well as covering frontier research in theoretical physics.

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This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

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Introduction.- The Euler-Lagrange equations and Noether´s theorem.- Scalar fields.- Vector fields.- Relativistic spinor fields.- The quantum theory of free fields.- Perturbative expansion in the phi 4 4 model.- Renormalization.- Renormalization group.- Relativistic invariance and the spectral decomposition of G(2).- Paths integrals in QFT.- The perturbative expansion for non-Abelian gauge fields.- The simplest supersymmetric models.- Anomalies.- Appendix: Some facts about generalized functions.

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From the reviews:
"This new and modern textbook stands out for its pedagogy ... and is based on an introductory course given to students at the University of Cracow in Poland. At the same time it is an excellent textbook for a first encounter with quantum field theory, treating a variety of topics that are only touched on in previous books with similar title." (Gert Roepstorff, Zentralblatt MATH, Vol. 1207, 2011)

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Both authors work in the Department of Field Theory at the Marian Smoluchowski Institute of Physics, Jagiellonian University, Cracow. They are experienced academic teachers specialized in theoretical and mathematical physics. Professor Henryk Arodz has published research papers on the Yang - Mills fields, topological defects, and several other topics in field theory and quantum mechanics. Dr. Leszek Hadasz has investigated, among other things, exactly solvable models with (super-)conformal symmetry and strings in non-critical dimensions.

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