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