A mathematical introduction to Dirac's formalism [electronic resource] / S.J.L. van Eijndhoven, J. de Graaf.

By: Eijndhoven, S. J. L. van (Stephanus J. L.), 1956-Contributor(s): Graaf, J. de (Johannes), 1942-Material type: Text

TextSeries: North-Holland mathematical library ; v. 36.Publication details: Amsterdam ; New York : New York, N.Y. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1986. Description: 1 online resource (xv, 430 p.)ISBN: 9780444701275; 0444701273Subject(s): Quantum theory | Dirac, P. A. M. (Paul Adrien Maurice), 1902-1984 | Dirac, P. A. M. (Paul Adrien Maurice), 1902-1984 | Th�eorie quantique | Dirac operatoren | Mecanica Quantica (Teoria Quantica) | Dirac, P. A. M. (Paul Adrien Maurice), 1902-1984 | Quantum theoryGenre/Form: Electronic books.Additional physical formats: Print version:: Mathematical introduction to Dirac's formalism.DDC classification: 530.1/2 LOC classification: QC174.12 | .E33 1986ebOnline resources: ScienceDirect | Volltext

Contents:

Some Basic Concepts and Developments in Sobolev Triples. Carleman Operators. A Measure Theoretical Sobolev Lemma. Dirac Bases. The Generalized Eigenvalue Problem for Self-Adjoint Operators. Direct Resolutions in Sobolev Triples. -- A Theory of Generalized Functions. Analyticity Spaces, Trajectory Spaces and Their Duality. Linear Mappings, Tensor Products and Kernel Theorems. Illustrations of Analyticity Spaces and Trajectory Spaces. The Concept of Dirac Bases Lifted to Trajectory Spaces. -- A Mathematical Interpretation of Dirac's Formalism. Dirac's Formalism According to Dirac and its Relations with Linear Algebra. A Mathematical Interpretation of Dirac's Bracket Formalism. The Free Field Operator Formalism.

Summary: This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part. The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.

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This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part. The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.

Includes bibliographical references (p. 417-423) and index.

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