General tensor indices

[Krzmbrzl]

Tensor objects (or more generally: anything fulfilling the AbstractTensor concept) are expected to divide their indices into bra and ket indices. There seems to be a connection (at least notation-wise) that bra indices correspond to creator indices and ket indices correspond to annihilator indices.

However, there are situations in which one would want to introduce a tensor object that has indices that are not connected to either a creator or annihilator operator (and would thus neither really fit into the bra or the ket group). Examples of where such tensors may enter are tensor decompositions like e.g. density fitting (resolution of the identity):
$g^{pq}_{rs} \approx B^p_r(Q) B^q_s(Q) - B^p_s(Q) B^q_r(Q)$
where B are the DF tensors and Q is an index in the auxiliary basis that is used for the DF approximation. This kind of decomposition is only performed on the actual (numeric) tensor object and therefore never appears in the second-quantized formalism and thus is not associated with a creator or annihilator.

While to my understanding the assignment of indices in tensor objects is only for notational purposes (when e.g. exporting to LaTeX), it'd be nice to conceptually keep the creator/annihilator association of tensor indices.

Therefore, I am proposing to extend the tensor concept to support general indices (neither creator nor annihilator).

[Krzmbrzl]

@evaleev any opposition to me implementing this?

[Krzmbrzl]

@bimalgaudel do you happen to know whether anyone in your group is working on something like this already or of some work that would conflict with this suggestion?

[bimalgaudel]

@bimalgaudel do you happen to know whether anyone in your group is working on something like this already or of some work that would conflict with this suggestion?

I believe no one is working to generalize the index type.

[Krzmbrzl]

Great, thank you! In that case I will start the implementation (presumably) within this week