spin7_vanishing
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| spin7_vanishing [2023/05/15 10:28] – spencer | spin7_vanishing [2023/05/15 10:32] (current) – spencer | ||
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| **Lemma 3:** $\ker D = \ker D^7 \cap \ker D^{21}$, the kernels being in $\Gamma(S^+ \otimes E)$. | **Lemma 3:** $\ker D = \ker D^7 \cap \ker D^{21}$, the kernels being in $\Gamma(S^+ \otimes E)$. | ||
| + | We have $|D\psi|^2 = |D^7 \psi|^2 + |D^{21}\psi|^2 + 2\langle D^7\psi, D^{21}\psi\rangle$. | ||
| + | It suffices (by the assumption that Clifford multiplication commutes with derivatives) to consider $\psi \in S^+_1$; but then the cross term vanishes a priori | ||
| <WRAP center round todo 60%> | <WRAP center round todo 60%> | ||
| - | **Proof:** Elided, for now | + | do this more carefully later |
| </ | </ | ||
spin7_vanishing.1684160935.txt.gz · Last modified: by spencer