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{{Quantum book backlink|Advanced and frontier topics}}
'''Supersymmetry''' (SUSY) is a theoretical symmetry that relates bosons and fermions. It extends quantum field theory by introducing transformations that map particles of integer spin to particles of half-integer spin and vice versa.<ref>{{cite book |last=Weinberg |first=Steven |title=The Quantum Theory of Fields, Vol. 3: Supersymmetry |publisher=Cambridge University Press |year=2000}}</ref>

In supersymmetric theories, each particle has a corresponding '''superpartner''' with different spin but otherwise similar properties.
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Supersymmetry: schematic relation between bosons and fermions via symmetry transformations, with corresponding superpartner fields.
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=Quantum Supersymmetry=
=== Supersymmetry transformations ===

Supersymmetry is generated by operators <math>Q</math> that transform bosonic states into fermionic states:

<math>
Q | \text{boson} \rangle = | \text{fermion} \rangle.
</math>

These operators extend the symmetry structure of spacetime and combine internal symmetries with spacetime symmetries.

The supersymmetry algebra includes relations of the form:

<math>
\{Q, Q^\dagger\} \propto P_\mu,
</math>

where <math>P_\mu</math> is the generator of spacetime translations.

=== Superpartners ===

In supersymmetric models, every known particle has a corresponding superpartner:

* fermions ↔ bosonic superpartners
* bosons ↔ fermionic superpartners

Examples include:

* electron → selectron
* quark → squark
* photon → photino

These superpartners have the same quantum numbers except for spin.

No superpartners have yet been observed experimentally.
=== Supersymmetry breaking ===

If supersymmetry were exact, particles and their superpartners would have identical masses. Since no such partners have been observed, supersymmetry must be '''broken''' in nature.

Supersymmetry breaking introduces mass differences between particles and their superpartners.

Various mechanisms have been proposed, including:

* spontaneous symmetry breaking
* soft breaking terms in the Lagrangian

These mechanisms allow supersymmetry to remain a useful theoretical framework while being consistent with experimental observations.<ref>{{cite book |last=Wess |first=Julius |last2=Bagger |first2=Jonathan |title=Supersymmetry and Supergravity |publisher=Princeton University Press |year=1992}}</ref>

=== Physical significance ===

Supersymmetry plays an important role in modern theoretical physics:

* it provides candidates for dark matter (e.g. neutralino),
* it improves the behavior of quantum field theories at high energies,
* it appears naturally in string theory.

Although not yet experimentally confirmed, supersymmetry remains a central idea in attempts to unify fundamental interactions.

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Supersymmetry|1}}

Physics:Quantum Supersymmetry - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template