Conformal Invariance in Quantum Mechanics
TLDR
In this paper, the properties of a field theory in one over-all time dimension, invariant under the full conformal group, are studied in detail, and a compact operator, which is not the Hamiltonian, is diagonalized and used to solve the problem of motion, providing a discrete spectrum and normalizable eigenstates.Abstract:
The properties of a field theory in one over-all time dimension, invariant under the full conformal group, are studied in detail. A compact operator, which is not the Hamiltonian, is diagonalized and used to solve the problem of motion, providing a discrete spectrum and normalizable eigenstates. The role of the physical parameters present in the model is discussed, mainly in connection with a semi-classical approximation.read more
Citations
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Remarks on the Sachdev-Ye-Kitaev model
Juan Maldacena,Douglas Stanford +1 more
TL;DR: In this paper, the authors studied the quantum mechanical model of $N$ Majorana fermions with random interactions of a few Fermions at a time (Sachdev-Ye-Kitaev model) in the large N$ limit.
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Comments on string theory backgrounds with non-relativistic conformal symmetry
TL;DR: In this article, the authors consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories and compute the thermodynamic properties of the system.
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Liouville Field Theory — A decade after the revolution
TL;DR: In this paper, a review of the recent developments of the Liouville field theory and its matrix model dual is presented, which includes some original material such as the derivation of the conjectured dual action for the N = 2 LiOUville theory from other known dualities and the comparison of the cross-cap state with the c = 0 unoriented matrix model.
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Light-front holographic QCD and emerging confinement
TL;DR: In this paper, a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in higher-dimensional anti-de Sitter space is presented.
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Local bulk operators in AdS/CFT correspondence : A boundary view of horizons and locality
TL;DR: In this paper, the authors developed the representation of local bulk fields in anti-de Sitter space by nonlocal operators on the boundary, working in the semiclassical limit and using ${\mathrm{AdS}}_{2}$ as their main example.
References
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A new approach to conformal invariant field theories
TL;DR: In this article, a new approach to conformal invariant field theories is presented, which is to introduce a fundamental scale of hadron phenomena by means of a dilatation non-invariant vacuum state in the framework of a scale invariant Lagrangian field theory.
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On the treatment of singular bethe-salpeter equations
TL;DR: In this article, the properties of the bound-state solutions of the BetheSalpeter equation in the ladder approximation are investigated in the case of potentials strongly singular at the origin and the analogy with potential scattering and the connexion to field theory are discussed.