Felix Berezin: Life And Death Of The Mastermind Of Supermathematics
Felix Berezin: Life And Death Of The Mastermind Of Supermathematics

Author: Misha Shifman

Publisher: World Scientific

Published: 2007-04-27

Total Pages: 258

ISBN-13: 9814476072

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Felix Berezin was an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. The integral over the anticommuting Grassmann variables that he introduced in the 1960s laid the foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him, as is the closely related construction of the Berezinian, which may be regarded as the superanalog of the determinant.This book features a masterfully written memoir by Berezin's widow, Elena Karpel, who narrates a remarkable account of Berezin's life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, Berezin's accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos.

Felix Berezin
Felix Berezin

Author: Mikhail A. Shifman

Publisher: World Scientific

Published: 2007

Total Pages: 258

ISBN-13: 9812705325

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Felix Berezin was an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. The integral over the anticommuting Grassmann variables that he introduced in the 1960s laid the foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him, as is the closely related construction of the Berezinian, which may be regarded as the superanalog of the determinant.This book features a masterfully written memoir by Berezin's widow, Elena Karpel, who narrates a remarkable account of Berezin's life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, Berezin's accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos.

Quantum Field Theory Ii
Quantum Field Theory Ii

Author: Misha Shifman

Publisher: World Scientific

Published: 2019-03-12

Total Pages: 319

ISBN-13: 9813234202

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This textbook grew out of lecture notes the author used in delivering a quantum field theory (QFT) course for students (both in high energy physics and condensed matter) who already had an initial exposure to the subject.It begins with the path integral method of quantization presented in a systematic and clear-cut manner. Perturbation theory is generalized beyond tree level, to include radiative corrections (loops). Renormalization procedures and the Wilsonian renormalization group (RG flow) are discussed, asymptotic freedom of non-Abelian gauge theories is derived, and some applications in Quantum Chromodynamics (QCD) are considered, with a brief digression into the Standard Model (SM). The SM case requires a study of the spontaneous breaking of gauge symmetry, a phenomenon which would be more appropriate to call 'Higgsing of the gauge bosons.' Other regimes attainable in gauge theories are explained as well. In the condensed matter part, the Heisenberg and Ising model are discussed. The present textbook differs from many others in that it is relatively concise and, at the same time, teaches students to carry out actual calculations which they may encounter in QFT-related applications.

Mathematical Cultures
Mathematical Cultures

Author: Brendan Larvor

Publisher: Birkhäuser

Published: 2016-05-25

Total Pages: 457

ISBN-13: 3319285823

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This collection presents significant contributions from an international network project on mathematical cultures, including essays from leading scholars in the history and philosophy of mathematics and mathematics education.​ Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematical research and teaching, and great variation in the place of mathematics in the larger cultures that mathematical practitioners belong to. The reflections on mathematical cultures collected in this book are of interest to mathematicians, philosophers, historians, sociologists, cognitive scientists and mathematics educators.

Toeplitz Matrices and Operators
Toeplitz Matrices and Operators

Author: Nikolaï Nikolski

Publisher: Cambridge University Press

Published: 2020-01-02

Total Pages: 453

ISBN-13: 1108187579

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The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.

Mathematical Analysis and Applications—Plenary Lectures
Mathematical Analysis and Applications—Plenary Lectures

Author: Luigi G. Rodino

Publisher: Springer

Published: 2018-11-11

Total Pages: 212

ISBN-13: 3030008746

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This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis. The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics. Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

Physics In A Mad World
Physics In A Mad World

Author: Misha Shifman

Publisher: World Scientific

Published: 2015-08-28

Total Pages: 555

ISBN-13: 9814619310

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This book tells captivating stories of misadventures of two renowned theoretical physicists in the Soviet Union. The first part is devoted to Friedrich (Fritz) Houtermans, an outstanding Dutch-Austrian-German physicist who was the first to suggest that the source of stars' energy is thermonuclear fusion, and also made a number of other important contributions to cosmochemistry and geochemistry. In 1935, Houtermans, a German communist, in an attempt to save his life from Hilter's Gestapo, fled to the Soviet Union. He took up an appointment at the Kharkov Physico-Technical Institute, working there for two years with the Russian physicist Valentin P Fomin. In the Great Purge of 1937, Houtermans was arrested in December by the NKVD (Soviet Secret Police, KGB's predecessor). He was tortured, and confessed to being a Trotskyist plotter and German spy, out of fear of threats against his wife Charlotte. However, Charlotte had already escaped from the Soviet Union to Denmark, after which she went to England and finally the USA. As a result of the Hilter-Stalin Pact of 1939, Houtermans was turned over to the Gestapo in May 1940 and imprisoned in Berlin.The second part consists of two essays that narrate the life story of Yuri Golfand, one of the codiscoverers of supersymmetry, a major discovery in theoretical physics in the 20th century. In 1973, just two years after the publication of his seminal paper, he was fired from the Lebedev Physics Institute in Moscow. Because of his Jewish origin he could find no job. Under such circumstances, he applied for an exit visa to Israel, but his application was denied. Yuri Golfand became a refusnik and joined the Human rights movement, along with two other prominent physicists, Andrei Sakharov and Yuri Orlov. To earn his living, he had to do manual work, repeatedly being intimidated by KGB. Only 18 years later, shortly before the demise of the Soviet Union, did he obtain permission to leave the country, emigrating to Israel in 1990.These personal life stories of two outstanding theorists are interwined with the tragedies of the 20th century and make for compelling reading.

Advanced Topics in Quantum Field Theory
Advanced Topics in Quantum Field Theory

Author: M. Shifman

Publisher: Cambridge University Press

Published: 2012-01-19

Total Pages: 641

ISBN-13: 0521190843

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Devoted specifically to modern field theory, this is an indispensable book for graduate students and researchers in theoretical physics. It emphasizes nonperturbative phenomena and supersymmetry, and discusses various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective.

Advanced Topics in Quantum Field Theory
Advanced Topics in Quantum Field Theory

Author: Mikhail Shifman

Publisher: Cambridge University Press

Published: 2022-04-28

Total Pages: 740

ISBN-13: 1108882080

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Quantum field theory is the basis of our modern description of physical phenomena at the fundamental level. This systematic and comprehensive text emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. This Second Edition is revised to include topics developed in the last decade, including higher-form global symmetries and their applications, anomalies in supersymmetric theories beyond Ferrara–Zumino, and non-Abelian supersymmetric vortex strings. A new final part is added, presenting more than 90 problems with detailed solutions, allowing students to check their understanding of the acquired knowledge and providing extra details to supplement the main text descriptions. This an indispensable book for graduate students and researchers in theoretical physics.

Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications
Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications

Author: Pavel Mnev

Publisher: American Mathematical Soc.

Published: 2019-08-20

Total Pages: 200

ISBN-13: 1470452715

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This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.