Abstract
Nature is certainly Poincaré invariant. However it is possible that her forces possess a much higher degree of space-time invariance than we have heretofore realized, such as invariance under transformations which relate fermions and bosons, so-called supersymmetry transformations(1). As will be explained below, exact supersymmetry of the forces (i.e., of the Lagrangian) as well as of the physical states requires bosons and fermions to come in mass-degenerate multiplets; evidently, nature does not exhibit such behavior. However it is nonetheless possible that nature is supersymmetric but that this is not manifest through degeneracy between bosons and fermions. Such a state of affairs is called spontaneously broken supersymmetry and occurs when the lowest energy state (the vacuum) is not super-symmetric even though the forces are(2).
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References and Footnotes
For an introduction to supersymmetry and a more complete list of references, see, e.g., S. Ferrara, Erice Lecture Notes, Aug. 1978 (CERN preprint TH2514) and
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For example, nature— in particular electromagnetism—is rotation invariant; however if one were living inside a huge ferromagnet, the essential rotation invariance of the fundamental interactions would not be trivially apparent: we would say that the “vacuum” (here the interior of the ferromagnet) did not possess the rotation invariance, even though the fundamental interactions do.
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© 1980 Plenum Press, New York
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Farrar, G.R. (1980). Supersymmetry in Nature. In: Zichichi, A. (eds) The New Aspects of Subnuclear Physics. The Subnuclear Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9170-2_2
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