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Title: Supersymmetry and Ghosts in Quantum Mechanics
Authors: Robert, Didier
Keywords: Supersymmetric Quantum Mechanics
Hamiltonian and Lagrangian Mechanics
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 34, No 1, (2008), 329p-354p
Abstract: A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯] + m2), in order to eliminate the divergences occuring in quantum field theory. But then the Hamiltonian of the system, obtained by second quantization, has large negative energies called "ghosts" by physicists. We report here on a joint work with A. Smilga (SUBATECH, Nantes) where we consider a similar problem for some models in quantum mechanics which are invariant under supersymmetric transformations. We show in particular that "ghosts" are still present.
Description: 2000 Mathematics Subject Classification: 81Q60, 35Q40.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 1

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