One can derive the important results of relativistic quantum theory (or qft) without much using bra-ket notation. However, I think if one wants a deep mathematical understanding, it is better to use bra-ket notation throughout. A Construction of Full QED Using Finite Dimensional Hilbert Space

One can derive the important results of relativistic quantum theory (or qft) without much using bra-ket notation. However, I think if one wants a deep mathematical understanding, it is better to use bra-ket notation throughout. I have done this in A Construction of Full QED Using Finite Dimensional Hilbert Space