Hamiltonian deformations in quantum mechanics, $T\bar T$, and SYK

Understand

Motivated by $T\bar T$, we introduce and study a wide class of solvable deformations of quantum-mechanical theories.

• These deformations map the Hamiltonian to a function of itself.
• We solve these theories by computing all finite-temperature correlation functions of the deformed theory in terms of the correlators of the undeformed theory.
• Applications to AdS/CFT, SYK, and the Schwarzian theory are considered.