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7.3: Internal and Space-Time Symmetries

Last updated

Aug 9, 2024
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- 7.2: Lorenz and Poincaré Invariance
- 7.4: Discrete Symmetries

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Above I have mentioned angular momentum, the vector product of position and momentum. This is defined in terms of properties of space (or to be more generous, of space-time). But we know that many particles carry the spin of the particle to form the total angular momentum,

${\vec{J}} = {\vec{L}} + {\vec{S}}. \nonumber$ The invariance of the dynamics is such that

${\vec{J}}$ is the conserved quantity, which means that we should not just rotate in ordinary space, but in the abstract “intrinsic space” where

${\vec{S}}$ is defined. This is something that will occur several times again, where a symmetry has a combination of a space-time and intrinsic part.

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