> Lie groups are the reason why it is better to represent gamma matrices as (Lorentz, Spinor, Spinor), the (Lorentz)-matrix representation loses the spinor-type transformation properties.
Why? the spinor transformations appear in matrix form S G(m) S**-1 = L(m, -n) G(n) On Monday, September 16, 2013 7:03:55 PM UTC+2, F. B. wrote: > > Further considerations: > > > - soon there will be a PR to add auto-matrix indices capabilities. In > the construction of a tensor, indices marked by True instead of an index > symbol will be considered auto-matrix indices, they behave upon > multiplication with other tensors as matrices or vectors (there can be 0, > 1 > or 2 automatrix indices for each TensorIndexType, 1 => vector behavior, > 2=> > matrix behavior). A tensor can have many automatrix indices, it is > important they are applied on different TensorIndexType. > - gamma matrices will have default auto-matrix behavior on their > spinor indices. > - tensor indices are conceptually strictly related to representations > of Lie groups, in the future we could generate TensorIndexType instances > from an object representing a representation of a Lie group. > - Lie groups are the reason why it is better to represent gamma > matrices as (Lorentz, Spinor, Spinor), the (Lorentz)-matrix representation > loses the spinor-type transformation properties. > - What happens on numerical indices? My guess is that a tensor gets > reduced in its rank. E.g. *GammaMatrix(U(3))*, this means that in a > certain basis we are representing gamma^3 covariant. Operators U( ) and D( > ) (up and down) need to be introduced. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
