Clifford Algebras in Physics by M. Rausch de Traubenberg

By M. Rausch de Traubenberg

We research in short a few homes of actual Clifford algebras and establish them as matrix algebras. We then express that the illustration area on which Clifford algebras act are spinors and we research in info matrix representations. the right constitution of those matrices offers upward push to the kind of spinors one is ready to build in a given space-time size: Majorana or Weyl. homes of spinors also are studied. We eventually convey how Clifford algebras permit us to build supersymmetric extensions of the Poincar\'e algebra. a different realization to the 4, ten and eleven-dimensional space-times is given. We then examine the representations of the thought of supersymmetric algebras and convey that illustration areas include an equivalent variety of bosons and fermions. Supersymmetry seems to be a symmetry which combines non-trivially the bosons and the fermions because one multiplet includes bosons and fermions jointly. We additionally exhibit how supersymmetry in 4 and ten dimensions are regarding 11 dimensional supersymmetry by way of compactification or dimensional reduction.

https://arxiv.org/abs/hep-th/0506011

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1 1 To identify the particle content of the various multiplet, we have to keep in mind that a massless particle of spin s is constituted of a state of helicity s and a state of helicity −s. For instance a left-handed massless electron is constituted of a state of helicity 1/2 and a state of helicity −1/2. The former can be interpreted as a left-handed electron of helicity − 21 and the latter as its corresponding anti-particle state the left-handed positron of helicity 1 e group, the first multiplet 2 .

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