Super-Poincaré Algebra
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras, and hence are Lie superalgebra. Thus a super-Poincaré algebra is a Z2 graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutatio...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras, and hence are Lie superalgebra. Thus a super-Poincaré algebra is a Z2 graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part. The simplest supersymmetric extension of the Poincaré algebra contains two Weyl spinors with the following anti-commutation relation: {Q_{alpha}, bar Q_{dot{beta}}} = 2{sigma^mu}_{alphadot{beta}}P_mu and all other anti-commutation relations between the Qs and Ps vanish. In the above expression P are the generators of translation and are the Pauli matrices.
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