# Implications of Conformal Symmetry in Quantum Mechanics

@article{Okazaki2017ImplicationsOC, title={Implications of Conformal Symmetry in Quantum Mechanics}, author={Tadashi Okazaki}, journal={Physical Review D}, year={2017}, volume={96}, pages={066030} }

In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics there exist bounds on scaling dimensions of the physical states and the gauge operators.

## 12 Citations

### Conformal quantum mechanics as a Floquet-Dirac system

- Physics
- 2021

Conformal quantum mechanics has been proposed to be the CFT1 dual to AdS2. The N -point correlation function that satisfy conformal constraints have been constructed from a non-conformal vacuum and…

### Conformal quantum mechanics and sine-square deformation

- PhysicsProgress of Theoretical and Experimental Physics
- 2018

We revisit conformal quantum mechanics (CQM) from the perspective of sine-square deformation (SSD) and the entanglement Hamiltonian. The operators that correspond to SSD and the entanglement…

### Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type

- Mathematics
- 2018

We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which is a semi-direct…

### Conformal quantum mechanics of causal diamonds

- Physics
- 2020

It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing…

### Protected SL(2,ℝ) symmetry in quantum cosmology

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2019

The polymer quantization of cosmological backgrounds provides an alternative path to the original Wheeler-de Witt (WdW) quantum cosmology, based on a different representation the commutation…

### Symmetry enhancement in RCFT II

- Physics
- 2022

We explain when and why symmetries enhance in fermionic rational conformal ﬁeld theories. In order to achieve the goal, we ﬁrst clarify invariants under renormalization group ﬂows. In particular, we…

### The AdS𝜃2/CFT1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence

- MathematicsInternational Journal of Modern Physics A
- 2022

A consistent QM / NCG duality is put forward as a model for the AdS 2 / CFT 1 correspondence. This is a duality/correspondence between 1) the dAFF conformal quantum mechanics (QM) on the boundary…

### Cosmology as a CFT1

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We show that the simplest FLRW cosmological system consisting in the homo- geneous and isotropic massless Einstein-Scalar system enjoys a hidden conformal symmetry under the 1D conformal…

### Klein four-group and Darboux duality in conformal mechanics

- MathematicsPhysical Review D
- 2019

The Klein four-group symmetry of the eigenvalue problem equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with coupling constant $g=\nu(\nu+1)\geq -1/4$ undergoes a complete…

### The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes

- Physics
- 2021

In this article we present the construction of noncommutative AdS 2 θ black hole and its four-dimensional Yang-Mills IKKT-type matrix model which includes two competing Myers term one responsible for…

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