Preprint typeset in JHEP style - HYPER VERSION

2 Superalgebra 2.1 Gamma Matrices and Spinors To make the SO(3) ×SO(6) structure of the M-theory on a pp-wave manifest, we write the nine dimensional gamma matrices in terms of the three and six dimensional ones, σi,γa Γi = σi ⊗γ(7) for i= 1,2,3 Γa = 1 ⊗γa for a= 4,5,6,7,8,9. (1) Machine Learning N = 8 = 5 Gauged Supergravity D A Useful Set of SO(7) Gamma matrices We have already seen that the SO(7) gamma matrices are used to translate between the USp(8) and the SL(6;R) SL(2;R) basis. In this section, we give an explicit construction of the SO(7) gamma matrices that we use in our code. A useful discussion of related ideas can be found in [18]. Those Physicists And Their "Physics Proofs" | Small

## Problem 1: As shown in class the Dirac matrices must satisfy the anti-commutator relationships: {αi,αj} = 2δij, { i, } = 0 with 2 = 1 I. Show that the i, are Hermitian, traceless matrices with eigenvalues ±1 and even dimensionality. II.Show that, as long as the mass term is not zero and the matrix is needed, there is

Pauli matrices - Wikipedia Algebraic properties. All three of the Pauli matrices can be compacted into a single expression: = (− + −) where i = √ −1 is the imaginary unit, and δ ab is the Kronecker delta, which equals +1 if a = b and 0 otherwise. This expression is useful for "selecting" any one of the matrices numerically by substituting values of a = 1, 2, 3, in turn useful when any of the matrices (but no

### Gravitational waves in massive conformal gravity

2 Superalgebra 2.1 Gamma Matrices and Spinors To make the SO(3) ×SO(6) structure of the M-theory on a pp-wave manifest, we write the nine dimensional gamma matrices in terms of the three and six dimensional ones, σi,γa Γi = σi ⊗γ(7) for i= 1,2,3 Γa = 1 ⊗γa for a= 4,5,6,7,8,9. (1) Machine Learning N = 8 = 5 Gauged Supergravity