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}
}
  • T. Okazaki
  • Published 2 April 2017
  • Physics
  • Physical Review D
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. 

Figures from this paper

Conformal quantum mechanics as a Floquet-Dirac system

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

  • T. Tada
  • Physics
    Progress 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

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

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

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

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

  • B. Ydri
  • Mathematics
    International 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

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

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

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

References

SHOWING 1-10 OF 43 REFERENCES

Whittaker vector, Wheeler-DeWitt equation, and the gravity dual of conformal quantum mechanics

We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying classical Lagrangian. We show that a generating function of expectation values among two

Conformal quantum mechanics as the CFT1 dual to AdS2

Quantum Hall states as matrix Chern-Simons theory

We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the

Entanglement entropy and negative energy in two dimensions

It is well known that quantum effects can produce negative energy densities, though for limited times. Here we show in the context of two-dimensional CFT that such negative energy densities are

Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces

This contribution to the proceedings of the 1999 NATO ASI on Quantum Geometry at Akureyri, Iceland, is based on notes of lectures given by A. Strominger. Topics include N-particle conformal quantum

Nonhamiltonian approach to conformal quantum field theory

A requirement of completeness of the operator set involved in the theory at small distances is formulated which replaces the unitarity condition of the S- matrix in the usual theory. Explicit

Superconformal quantum mechanics

Conformal blocks for the four-point function in conformal quantum mechanics

Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, which realizes the SO(2,1)

Duality in quantum field theory

Weyl consistency conditions in non-relativistic quantum field theory

A bstractWeyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl