Can someone outline the difference between supersymmetry and supersymmetric quantum mechanics? I often hear the two used interchangeably but I'm almost certain they are not the same.

  • 2
    $\begingroup$ Can you be more specific since the articles you linked to already contain most of the standard statements users are liable to make here? Related: physics.stackexchange.com/q/53482 $\endgroup$ Jul 7 '14 at 0:55

From a little bit of reading, I believe that "Supersymmetry" refers to the relativistic formulation of the extra symmetries between bosons and fermions, and "supersymmetric quantum mechanics" refers to the non-relativistic formulation of the same symmetry.

In other words, one is compatible with special relativity and deal with fields (SUSY) and one primarily uses the Schrodinger equation and deals with particles (supersymmetric quantum mechanics).

  • $\begingroup$ What about wordline supersymmetry ? (see references in nLab). I think this is an alternative description of a relativist spinning particle in a background field. $\endgroup$
    – Trimok
    Jul 7 '14 at 8:54
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    $\begingroup$ Right, it appears that worldline supersymmetry is SUSY, not supersymmetric quantum mechanics. $\endgroup$
    – levitopher
    Jul 7 '14 at 17:04

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