Supersymmetry algebraIn theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of N real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Łopuszański–Sohnius theorem. When N>1 the algebra is said to have extended supersymmetry.
Fock stateIn quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions.
SuperspaceSuperspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom. The word "superspace" was first used by John Wheeler in an unrelated sense to describe the configuration space of general relativity; for example, this usage may be seen in his 1973 textbook Gravitation.
Opérateur de CasimirEn mathématiques, et plus spécifiquement en algèbre, l'opérateur de Casimir est un opérateur particulier. Plus précisément, étant donné une algèbre de Lie munie d'une forme bilinéaire non-dégénérée et invariante, et une représentation de dimension finie, l'opérateur de Casimir est une application linéaire continue particulière sur l'espace vectoriel de la représentation. Cet opérateur commute avec la représentation. Pour l'algèbre de Lie et la représentation étudiées, cet opérateur joue le rôle du laplacien.
Wigner's classificationIn mathematics and theoretical physics, Wigner's classification is a classification of the nonnegative energy irreducible unitary representations of the Poincaré group which have either finite or zero mass eigenvalues. (Since this group is noncompact, these unitary representations are infinite-dimensional.) It was introduced by Eugene Wigner, to classify particles and fields in physics—see the article particle physics and representation theory. It relies on the stabilizer subgroups of that group, dubbed the Wigner little groups of various mass states.
