4 items with this tag.
Gamma matrices gamma-matrices algebras bilinear-products Definition From the relation $\phi^k B^{i^\prime}{\phantom{i^\prime} k i} = \Lambda^{i^\prime}{\phantom{i^\prime} i}$ , we see that $\left{ B^{i^\prime}_{\phantom{i^\prime} k i} \right}k$ forms a basis for $\Lambda^{i^\prime}{\phantom{i^\prime...
Complex numbers and quaternions algebras bilinear-products Complex numbers 2-dimensional orthogonal group Complex numbers are one of the most well-known algebras-over-fields, in use ever since people tried to solve ‘unsolvable’ polynomial equations, such as $i^2 = -1$ .
Algebras algebras bilinear-products J tensor Definition In the component representation of bilinear products as linear maps, we have a product of Jacobian components on the right hand side: $\Lambda^{I^\prime}{\phantom{I^\prime} I} \Lambda^{J}{\phantom{L} J^\prime} = \Lambda^{i_1^\prime}{\phantom{i_...
Noether’s theorem noether-theorem symmetries bilinear-products algebras Derivation Let spacetime be parameterized by an arbitrary scalar $\alpha$.