advanced_tools:topology:cocycles
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advanced_tools:topology:cocycles [2017/12/20 10:34] jakobadmin created |
advanced_tools:topology:cocycles [2017/12/20 10:35] (current) jakobadmin [Student] |
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| - | Every particle transforms under spatial rotations according to a [[group_theory:notions:projective_representation|projective representation]] of the rotation group $SO(3)$. Cocycles appear in the definition of a projective representation. | + | Every particle transforms under spatial rotations according to a [[advanced_tools:group_theory:representation_theory:projective_representation|projective representation]] of the rotation group $SO(3)$. Cocycles appear in the definition of a projective representation. |
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| <blockquote> | <blockquote> | ||
| - | Because state vectors differing only by a phase are the same for certain purposes, it turns out that symmetries need not correspond to unitary representations; they can correspond to [[group_theory:notions:projective_representation|projective representations]], in which the rules of a representation hold only 'up to phases': | + | Because state vectors differing only by a phase are the same for certain purposes, it turns out that symmetries need not correspond to unitary representations; they can correspond to [[advanced_tools:group_theory:representation_theory:projective_representation|projective representations,]] in which the rules of a representation hold only 'up to phases': |
| $$ \rho(1) = e^{i\theta}, $$ | $$ \rho(1) = e^{i\theta}, $$ | ||
advanced_tools/topology/cocycles.1513762498.txt.gz ยท Last modified: 2017/12/20 09:34 (external edit)
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