Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
Bender and P.D
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Contrary to common belief, it is shown that theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototypical fourth-order derivative Pais-Uhlenbeck oscillator model is shown to be free of states of negative energy or negative norm. When correctly formulated (as a $\cP\cT$ symmetric theory), the theory determines its own Hilbert space and associated positive-definite inner product. In this Hilbert space the model is found to be a fully acceptable quantum-mechanical theory that exhibits unitary time evolution.
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A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
Quadratic gravity in 4D preserves unitarity because the extra spin-2 sector is a dual inverted harmonic oscillator with vanishing spectral density, yielding a principal-value propagator that satisfies the optical theorem with only virtual contributions.
Review of spectral noncommutative geometry applied to the Standard Model, including bosonic and fermionic actions, Euclidean vs Lorentz issues, and going beyond the SM.
citing papers explorer
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Quantum mechanics with a ghost: Counterexamples to spectral denseness
Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
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Unitary Time Evolution and Vacuum for a Quantum Stable Ghost
A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
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Unitary Quadratic Quantum Gravity in 4D
Quadratic gravity in 4D preserves unitarity because the extra spin-2 sector is a dual inverted harmonic oscillator with vanishing spectral density, yielding a principal-value propagator that satisfies the optical theorem with only virtual contributions.
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Spectral Noncommutative Geometry, Standard Model and all that
Review of spectral noncommutative geometry applied to the Standard Model, including bosonic and fermionic actions, Euclidean vs Lorentz issues, and going beyond the SM.
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