An $xp$ model on $Ad{S}_2$ spacetime

Abstract

In this paper we formulate the $xp$ model on the AdS${}_2$ spacetime. We find that the spectrum of the Hamiltonian has positive and negative eigenvalues, whose absolute values are given by a harmonic oscillator spectrum, which in turn coincides with that of a massive Dirac fermion in AdS${}_2$. We extend this result to generic $xp$ models which are shown to be equivalent to a massive Dirac fermion on spacetimes whose metric depend of the $xp$ Hamiltonian. Finally, we construct the generators of the isometry group SO(2,1) of the AdS${}_2$ spacetime, and discuss the relation with conformal quantum mechanics.

24 pages, 1 figure, some comments and new references added

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• The Riemann zeros as spectrum and the Riemann hypothesis
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
• Duality constructions from quantum state manifolds
• Polymeric quantum mechanics and the zeros of the Riemann zeta function