Date of Award
Master of Science (M.S.)
Carl E. Wulfman
First Committee Member
Randall T. Swimm
Second Committee Member
Douglas B. Smith
Third Committee Member
William H. Ford
As was recognized by same of the most reputable physicists of the world such as Galilee and Einstein, the basic laws of physics must inevitably be founded upon invariance principles. Galilean and special relativity stand as historical landmarks that emphasize this message. It's no wonder that the great developments of modern physics (such as those in elementary particle physics) have been keyed upon this concept.
The modern formulation of classical mechanics (see Abraham and Marsden ) is based upon "qualitative" or geometric analysis. This is primarily due to the works of Poincare. Poincare showed the value of such geometric analysis in the solution of otherwise insoluble problems in stability theory. It seems that the insights of Poincare have proven fruitful by the now famous works of Kolmogorov, Arnold, and Moser. The concepts used in this geometric theory are again based upon invariance principles, or symmetries.
The work of Sophus Lie from 1873 to 1893 laid the groundwork for the analysis of invariance or symmetry principles in modern physics. His primary studies were those of partial differential equations. This led him to the study of the theory of transformations and inevitably to the analysis of abstract groups and differential geometry. Here we show same further applications of Lie group theory through the use of transformation groups. We emphasize the use of transformation invariance to find conservation laws and dynamical properties in chemical physics.
Nagao, Gregory G.. (1980). Determiningeons : a computer program for approximating lie generators admitted by dynamical systems. University of the Pacific, Thesis. https://scholarlycommons.pacific.edu/uop_etds/2028
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