Determinants and their applications in mathematical physics


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A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis.

Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before.

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Share your thoughts with other customers. We derive chiral anomalies as changes of a certain type of regularized determinants of Dirac operators defined on Euclidean space-time 2 n under infinitesimal chiral transformations. We study a relation between chiral anomalies and the topology of the space of invertible Dirac operators. A possible modification of our regularized determinant is discussed in connection with the chiral Schwinger model.

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Close mobile search navigation Article Navigation. Volume D45 V45 Available. More options. Find it at other libraries via WorldCat Limited preview. Contributor Dale, Paul. Bibliography Includes bibliographical references p. Contents Preface.


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It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries to the most recent 20th century developments. Several contributions have never been published before. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis.

The whole of Chapter 4 is devoted to particular determinants including alternants, Wronskians and Hankelians. The contents of Chapter 5 include the Cusick and Matsuno identities. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. They include the KdV, Toda and Einstein equations.


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Determinants and their applications in mathematical physics Determinants and their applications in mathematical physics
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Determinants and their applications in mathematical physics Determinants and their applications in mathematical physics
Determinants and their applications in mathematical physics Determinants and their applications in mathematical physics
Determinants and their applications in mathematical physics Determinants and their applications in mathematical physics
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