1. Lie algebras were introduced to study the concept of infinitesimal transformations . 2. This implies that infinitesimal transformations are transformed with a Hermitian operator. 3. Hermitian operators then follow for infinitesimal transformations of a classical polarization state. 4. The boost and rotation here are infinitesimal transformations because and rotation are small. 5. In mathematics, an "'infinitesimal transformation "'is a transformation. 6. One-parameter groups were introduced by Sophus Lie in 1893 to define infinitesimal transformations . 7. Lie algebras abstract the essential nature of infinitesimal transformations , and have become ubiquitous in mathematics. 8. Notice and are infinitesimal transformations because they involve a small increment in the relative velocity, while is not. 9. The third theorem on the list stated the Jacobi identity for the infinitesimal transformations of a local Lie group. 10. Thus, energy conservation requires that infinitesimal transformations of a polarization state occur through the action of a Hermitian operator.
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