Symplectic Matrices, First Order Systems And Special Relativity

Symplectic Matrices, First Order Systems And Special Relativity

By: Mark Kauderer (author)Hardback

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Description

The recent developments in canonical transforms, matrix theory, block Kronecker multiplications, and other areas are applied to extend and simplify results in the theory of first order systems and special relativity. Especially noteworthy are the author's results on Fourier transforms in dimensions lower than the surrounding space and his approach to the Doppler effect, which has never been published previously and supersedes previous works on this topic, which failed to solve the Doppler effect exactly. Some of the goals of this work are: to develop the theory of complex symmetric matrices as the rigorous foundations of first order systems, to exhibit in full generality the author's method of duality, and to discuss the neglected area of three dimensional effects in special relativity. The section on special relativity has been especially simplified so that it may be used as a beginning graduate text in this area. It includes the first full discussion of the Lorentz group in a book since Silberstein's pioneering 1913 treatment.

Contents

Part 1 Symplectic matrices: derivation of the symplectic conditions from the canonical commutation relations; symplectic group - the embedding theorem, the fundamental relation; the theory of types for minors and Fourier completeness; duality transformations; hyperdifferential representation of first order systems. Part 2 Fourier optics: derivation of the linear scalar transfer function for anisotropic media; optical implementation of the nonorthogonal group; acousto-optical signal processing; first order sources in Fourier optics - the generalized Gaussian Schell model source; the modes of first order systems. Part 3 Special relativity: canonical treatment of special relativity - the decomposition theorem; integral representation of special relativity; exact solution of the coincident Doppler effect; exact solution of the noncoincident Doppler effect; nonassociativity in special relativity - the relativistic vector addition law; the gamma calculus; the symplectic preserving group.

Product Details

  • ISBN13: 9789810208295
  • Format: Hardback
  • Number Of Pages: 344
  • ID: 9789810208295
  • ISBN10: 9810208294

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