A resonant ghostly 3D Pais-Uhlenbeck oscillator exhibits non-diagonalisable classical flow with Jordan chains of length three and a hidden u(2,1) spectrum-generating algebra upon quantization, with tri-Hamiltonian geometry but no positive-definite linear combination.
Spontaneous generation of the Newton constant in the renormalizable gravity theory
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The conformal supergravity is suggested as a realistic theory for gravity interactions. It displays the spontaneous breaking of the conformal symmetry which results in appearance of the term proportional to the scalar curvature R in the effective potential with respect to small metric fluctuations.
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Hidden $\mathfrak{u}(2,1)$ symmetry and Jordan chains in a resonant ghostly three-dimensional model
A resonant ghostly 3D Pais-Uhlenbeck oscillator exhibits non-diagonalisable classical flow with Jordan chains of length three and a hidden u(2,1) spectrum-generating algebra upon quantization, with tri-Hamiltonian geometry but no positive-definite linear combination.