Abstract
Supersymmetry at a susy harmonic oscillator, H(ω1, ω1), can be broken or restored in certain conditions and parameters, that are linked with thermal interaction and with a polynomial interactions of creation and annihilation operators. All possibles supersymmetric harmonic oscillators represented by a point (ω1, ω1) in the frequency space of the system, are in a two dimensional surface parametrized by the (ω2, α2), which we call s-surface, where α2 is the interaction parameter. The temperature in the s-surface are intended to be zero. Interaction with the thermal bath represented by the tilde Hilbert space from the doubling Hilbert space, establishes thermal oscillations that push the system from the s-surface. In such a way we can define the set of all supersymmetric harmonic oscillator or in a equivalent way the s-surface as a global standard reference for zero temperature.
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