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--- conformal_quantum_mechanics [2021/04/07 22:51]
Brian McPeak created
+++ conformal_quantum_mechanics [2021/04/09 16:19] (current)
Scott Lawrence
@@ Line 1: / Line 1: @@
+======Conformal quantum mechanics======
+{{tag>1d}}
 Haven't gotten to this yet. Sources:
   - Qualls CFT lectures [[https://arxiv.org/pdf/1511.04074.pdf|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]]
+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 $SO(2,1)$

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