- #1
shereen1
- 51
- 1
Dear All
Am trying to study supersymmetry algebra. We start by constructing the graded poincare algebra by considering the direct sum of the ordinary Poincare algebra L0 with a subspace L1 spanned by the spinor generators Qa where a runs from 1 to 4 ( L1 is not a lie algebra ). So now we have only 4 spinor generators. Then, i want to add the internal symmetry group to get the maximal symmetry of the S matrix. Here is my question. The internal symmetry group has dimension N of N generators Bl. Now we add N spinor generators . Then Q will have 2 indices one for the spinor part a and the other for the internal one. but initially L1 is 4 dimension so these spinors to which space belong?
Or should i from the beginning suppose that the L1 is spanned by 4N generators.
Thank you
Am trying to study supersymmetry algebra. We start by constructing the graded poincare algebra by considering the direct sum of the ordinary Poincare algebra L0 with a subspace L1 spanned by the spinor generators Qa where a runs from 1 to 4 ( L1 is not a lie algebra ). So now we have only 4 spinor generators. Then, i want to add the internal symmetry group to get the maximal symmetry of the S matrix. Here is my question. The internal symmetry group has dimension N of N generators Bl. Now we add N spinor generators . Then Q will have 2 indices one for the spinor part a and the other for the internal one. but initially L1 is 4 dimension so these spinors to which space belong?
Or should i from the beginning suppose that the L1 is spanned by 4N generators.
Thank you