# Supersymmetry and Ghosts in Quantum Mechanics

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 1, page 329-354
- ISSN: 1310-6600

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topRobert, Didier. "Supersymmetry and Ghosts in Quantum Mechanics." Serdica Mathematical Journal 34.1 (2008): 329-354. <http://eudml.org/doc/281418>.

@article{Robert2008,

abstract = {2000 Mathematics Subject Classification: 81Q60, 35Q40.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.},

author = {Robert, Didier},

journal = {Serdica Mathematical Journal},

keywords = {Supersymmetric Quantum Mechanics; Hamiltonian and Lagrangian Mechanics; Bosons; Fermions; supersymmetric quantum mechanics; Hamiltonian and Lagrangian mechanics; bosons and fermions},

language = {eng},

number = {1},

pages = {329-354},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Supersymmetry and Ghosts in Quantum Mechanics},

url = {http://eudml.org/doc/281418},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Robert, Didier

TI - Supersymmetry and Ghosts in Quantum Mechanics

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 1

SP - 329

EP - 354

AB - 2000 Mathematics Subject Classification: 81Q60, 35Q40.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.

LA - eng

KW - Supersymmetric Quantum Mechanics; Hamiltonian and Lagrangian Mechanics; Bosons; Fermions; supersymmetric quantum mechanics; Hamiltonian and Lagrangian mechanics; bosons and fermions

UR - http://eudml.org/doc/281418

ER -

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