In recent years a new type of symmetry, known as “supersymmetry,” has assumed considerable interest, because it appears to provide a channel for unifying the external and the internal symmetries. Whereas the external symmetries relate to our ideas of space and time and are associated with the notions of energy, linear momentum, and angular momentum (including spin), the internal symmetries are associated with perceived other properties of elementary particles, their electric charge, their isospin, strangeness, lepton and baryon number, color, charm, etc. Among elementary particles there are to be found families that combine bosons and fermions; accordingly, supersymmetry includes transformations that lead from bosonic to fermionic states, and vice versa. The term“supergravity” denotes theories in which supersymmetry is gauged and in which the external (space-time) symmetry is that of diffeomorphisms (rather than the Poincaré group), characteristic of general relativity.
KeywordsAssociative Algebra Clifford Algebra Ordinary Number Internal Symmetry Grassmann Algebra
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