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" Spinors in Physics "
by Jean Hladik.
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BL
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| Record Number
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573547
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b402766
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| Main Entry
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Hladik, Jean.
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| Title & Author
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Spinors in Physics\ by Jean Hladik.
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| Publication Statement
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New York, NY :: Springer New York :: Imprint: Springer,, 1999.
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| Series Statement
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Graduate Texts in Contemporary Physics,
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| ISBN
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9781461214885
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: 9781461271635
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| Contents
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I Spinors in Three-Dimensional Space -- 1 Two-Component Spinor Geometry -- 2 Spinors and SU (2) Group Representations -- 3 Spinor Representation of SO (3) -- 4 Pauli Spinors -- II Spinors in Four-Dimensional Space -- 5 The Lorentz Group -- 6 Representations of the Lorentz Groups -- 7 Dirac Spinors -- 8 Clifford and Lie Algebras -- Appendix: Groups and Their Representations -- A.1 The Definition of a Group -- A.1.1 Examples of Groups -- A.1.2 The Axioms Defining a Group -- A.1.3 Elementary Properties of Groups -- A.2 Linear Operators -- A.2.1 The Operator Representing an Element of a Group -- A.2.2 The Operators Acting on the Vectors of Geometric Space -- A.2.3 The Operators Acting on Wave Functions -- A.2.4 Operators Representing a Group -- A.3 Matrix Representations -- A.3.1 The Rotation Matrix Acting on the Vectors of a Three-Dimensional Space -- A.3.2 The Matrix of an Operator Acting on Functions -- A.3.3 The Matrices Representing the Elements of a Group -- A.4 Matrix Representations -- A.4.1 The Definition of a Matrix Representation -- A.4.2 The Fundamental Property of the Matrices of a Representation -- A.4.3 Representation by Regular Matrices -- A.4.4 Equivalent Representations -- A.5 Reducible and Irreducible Representations -- A.5.1 The Direct Sum of Two Vector Spaces -- A.5.2 The Direct Sum of Two Representations -- A.5.3 Irreducible Representations -- A.6 The Direct Product of Representations -- A.6.1 The Direct Product of Two Matrices -- A.6.2 Properties of Tensor Products of Matrices -- A.6.3 The Direct Product of Two Representations -- References.
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| Abstract
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Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles (including photons). Because of their relations to the rotation group SO(n) and the unitary group SU(n), the discussion should be of interest to applied mathematicians as well as physicists.
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Physics.
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Quantum theory.
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| Added Entry
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SpringerLink (Online service)
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