CFT Zoo

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conformal_quantum_mechanics [2021/04/07 22:52]
Brian McPeak 		conformal_quantum_mechanics [2021/04/09 16:19] (current)
Scott Lawrence
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 +======Conformal quantum mechanics======
 +
 +{{tag>1d}}
 +
 Haven't gotten to this yet. Sources: Haven't gotten to this yet. Sources:
   - Qualls CFT lectures [[https://arxiv.org/pdf/1511.04074.pdf|here]]   - Qualls CFT lectures [[https://arxiv.org/pdf/1511.04074.pdf|here]]
   - Model appears to have been introduced [[https://inspirehep.net/literature/108211|here]]   - Model appears to have been introduced [[https://inspirehep.net/literature/108211|here]]
   - discussion on the non-invariance of the ground state [[https://arxiv.org/pdf/1106.0726.pdf|here]]   - discussion on the non-invariance of the ground state [[https://arxiv.org/pdf/1106.0726.pdf|here]]
 +
 +The most general Lagrangian consistent with time and scale invariance is given by
 +%
 +\begin{align}
 +L = \frac{1}{2} \dot{Q}^2 - \frac{g^2}{2 Q^2}
 +\end{align}
 +%
 +This theory exhibits an $SL(2, \mathbb{R} \sim SO(2,1)$ symmetry. However, it does not have a normalizable ground state which is annihilated by all three of the generators of $SO(2,1)$ 
Last modified: 2021/04/07 22:52
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