Implications of Conformal Symmetry in Quantum Mechanics

Abstract

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.

25 pages, 2 figures; v3: published version in Physical Review D

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Cited by in corpus (11)

• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Conformal Quantum Mechanics and Sine-Square Deformation
• Conformal quantum mechanics of causal diamonds
• Klein four-group and Darboux duality in conformal mechanics
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Conformal quantum mechanics as a Floquet-Dirac system
• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey
• Cosmology as a CFT${}_1$
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes