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advanced_notions:thomas_precession [2019/06/10 10:15] jakobadmin [Abstract] |
advanced_notions:thomas_precession [2019/06/10 10:20] jakobadmin [Abstract] |
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+ | Abstractly, the Thomas precession is due to an additional rotation the spin of the particle pics up as a result of of the orbit movement. In this sense, the phenomenon is due to a [[advanced_tools:geometric_phase|geometric phase]]/Berry phase. | ||
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+ | From a group theoretic perspective, Thomas precession occurs because Lorentz boost do not commute. For example, we have | ||
+ | $$[K_y,\,K_x] = i\,J_z \, .$$ | ||
+ | The rotation that we get by combining boosts is known as a Wigner rotation. | ||
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<blockquote>{{ :advanced_notions:thomas_precession.jpg?nolink&200|}}[T]he revolution of the particle around the nucleus can be interpreted as a sequence of Lorentz boosts.[...] Abstractly, the effect is due to Wigner rotations [3] that appear in representations of the Poincaré group, so it is purely kinematical—it follows solely from space-time symmetries. <cite>https://arxiv.org/abs/1711.05753</cite></blockquote> | <blockquote>{{ :advanced_notions:thomas_precession.jpg?nolink&200|}}[T]he revolution of the particle around the nucleus can be interpreted as a sequence of Lorentz boosts.[...] Abstractly, the effect is due to Wigner rotations [3] that appear in representations of the Poincaré group, so it is purely kinematical—it follows solely from space-time symmetries. <cite>https://arxiv.org/abs/1711.05753</cite></blockquote> |