The Theory of Groups and Quantum Mechanics

Couverture
Courier Corporation, 1 janv. 1950 - 422 pages
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
 

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Table des matières

GROUPS AND THEIR REPRESENTATIONS
110
Extension to Closed Continuous Groups
163
Invariants and Covariants
170
Representation by Rotations of Ray Space
180
B The Lorentz Group
210
Energy and Momentum Remarks on the Interchange of Past
218
Electron in Spherically Symmetric Field
227
Selection Rules Fine Structure
233
Grouptheoretic Classification of Atomic Spectra
369
Determination of the Primitive Characters of u and
377
Calculation of Volume on
386
Branching Laws 369 377 386
391
PROOF OF AN INEQUALITY
393
A COMPOSITION PROPERTY OF GROUP CHARACTERS
395
A THEOREM CONCERNING NONDEGENERATE ANTISYMMETRIC BI LINEAR FORMS
397
BIBLIOGRAPHY
399

1o The Pauli Exclusion Principle and the Structure of
242
Quantization of the MaxwellDirac Field Equations
253
The Energy and Momentum Laws of Quantum Physics
264
Quantum Kinematics as an Abelian Group of Rotations
272
THE SYMMETRIC PERMUTATION GROUP AND THE ALGEBRA OF SYM
281
Explicit Algebraic Construction PAGE 358 362 13 Youngs Symmetry Operators
358
LIST OF OPERATIONAL SYMBOLS
409
LIST OF LETTERS HAVING A FIXED SIGNIFICANCE
410
INDEX
413
326
417
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À propos de l'auteur (1950)

Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.

Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.

In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."

"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl

Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science




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