Fermionic coordinates and supersymmetry in quantum mechanics

Salomonson, Per; Holten, J.W. van

doi:10.1016/0550-3213(82)90505-3

Cited by 271 publications

(143 citation statements)

References 4 publications

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“…The solutions for SO(6) scalars are X a = 0 for these instantons in the weak coupling theory. We can thereby write a "superpotential" [16], [17] for this supersymmetric quantum mechanics, for each fuzzy sphere vacuum:…”

Section: Instantons On the Gauge Theory Sidementioning

confidence: 99%

Instantons, supersymmetric vacua, and emergent geometries

Lin

2006

Phys. Rev. D

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We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on R × S 2 with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.

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Section: Instantons On the Gauge Theory Sidementioning

confidence: 99%

Instantons, supersymmetric vacua, and emergent geometries

Lin

2006

Phys. Rev. D

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“…Further the reflection and transmission coefficients (or phase shifts) for the hierarchy of Hamiltonians can be obtained in terms of R 1 , T 1 of the first Hamiltonian H 1 by a repeated use of eq. (30). In particular we find…”

Section: Factorization and The Hierarchy Of Hamiltoniansmentioning

confidence: 61%

“…(30) or (37). The breaking of SUSY can be described by a topological quantum number called the Witten index [12] which we will discuss later.…”

Section: Hamiltonian Formulation Of Supersymmetric Quantum Mechanicsmentioning

confidence: 99%

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Parasupersymmetry in quantum mechanics

Khare

1993

Journal of Mathematical Physics

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In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all 1 have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.

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“…The quantum mechanical instantons are expected to break the d = 1, N = ∈ supersymmetry. This is a known phenomenon in supersymmetric quantum mechanics [17,18].…”

Section: Eigenvalue Instantonsmentioning

confidence: 99%

Effective d = 2 supersymmetric lagrangians from d = 1 supermatrix models

1994

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We discuss d = 1, N = 2 supersymmetric matrix models and exhibit the associated d = 2 collective field theory in the limit of dense eigenvalues. From this theory we construct, by the addition of several new fields, a d = 2 supersymmetric effective field theory, which reduces to the collective field theory when the new fields are replaced with their vacuum expectation values. This effective theory is Poincare invariant and contains perturbative and non-perturbative information about the associated superstrings. We exhibit instanton solutions corresponding to the motion of single eigenvalues and discuss their possible role in supersymmetry breaking.

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Fermionic coordinates and supersymmetry in quantum mechanics

Cited by 271 publications

References 4 publications

Instantons, supersymmetric vacua, and emergent geometries

Instantons, supersymmetric vacua, and emergent geometries

Parasupersymmetry in quantum mechanics

Effective d = 2 supersymmetric lagrangians from d = 1 supermatrix models

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