Regularised integrals, sums, and traces : an analytic point of view
 Author/Creator
 Paycha, Sylvie.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 x, 190 p. : ill. ; 26 cm.
 Series
 University lecture series (Providence, R.I.) ; 59.
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QA351 .P29 2012

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QA351 .P29 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 "Regularization techniques" is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinitedimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and selfcontained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these "building blocks", one encounters many problems and ambiguities caused by various socalled anomalies, which are investigated and explained in detail. Nevertheless, it turns out that the corresponding canonical sums, integrals, sums, and traces are well behaved, thus making the regularization procedure possible and manageable. This new unified outlook on regularization techniques in various fields of mathematics and in quantum field theory can serve as an introduction for anyone from a beginning mathematician interested in the subject to an experienced physicist who wants to gain a unified outlook on techniques he/she uses on a daily basis.
(source: Nielsen Book Data)
Subjects
 Subject
 Functions, Zeta.
 Lfunctions.
 Convergence.
 Integrals.
 Number theory  Zeta and $L$functions: analytic theory  $\zeta (s)$ and $L(s, \chi)$.
 Sequences, series, summability  Convergence and divergence of infinite limiting processes  Convergence and divergence of integrals.
 Operator theory  Linear spaces and algebras of operators  Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
 Quantum theory  Quantum field theory; related classical field theories  Anomalies.
 Numerical analysis  Acceleration of convergence  EulerMaclaurin formula.
Bibliographic information
 Publication date
 2012
 Responsibility
 Sylvie Paycha.
 Series
 University lecture series ; v. 59
 ISBN
 9780821853672 (alk. paper)
 0821853678 (alk. paper)