Physics:Quantum Supersymmetry

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Supersymmetry: schematic relation between bosons and fermions via symmetry transformations, with corresponding superpartner fields.

Quantum Supersymmetry

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.[1]

In supersymmetric theories, each particle has a corresponding superpartner with different spin but otherwise similar properties.

Supersymmetry transformations

Supersymmetry is generated by operators Q that transform bosonic states into fermionic states:

Q|boson⟩=|fermion⟩.

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

The supersymmetry algebra includes relations of the form:

{Q,Q†}∝Pμ,

where Pμ 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.[2]

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

Foundations

Conceptual and interpretations

Mathematical and solvable systems

Symmetry and structure

Atomic and spectroscopy

Quantum wavefunctions and modes

Quantum information and computing

Quantum optics and experiments

Open quantum systems

Quantum field theory

Timeline

Advanced and frontier topics


References

  1. ↑ Weinberg, Steven (2000). The Quantum Theory of Fields, Vol. 3: Supersymmetry. Cambridge University Press. 
  2. ↑ Wess, Julius; Bagger, Jonathan (1992). Supersymmetry and Supergravity. Princeton University Press. 


Author: Harold Foppele





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