Thrice said:
A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you guys think.
There's nothing particularly great about Dirac's notation outside of, say, quantum mechanics and linear algebra. For example, given some vector space V(n,\mathbb{F}) with dual V^*(n,\mathbb{F}), we could choose to use Dirac's notation to denote an inner product between |\psi\rangle\in V(n,\mathbb{F}) and \langle\phi|\in V^*(n,\mathbb{F}) by
\langle\phi|\psi\rangle\in\mathbb{F}
However, in index notation you would choose a basis \{e_i\} for V(n,\mathbb{F}) and a corresponding dual basis \{\omega^i\} for V^*(n,\mathbb{F}). Then the inner product of the above quantities is
\phi_i\psi^i\in\mathbb{F}[/itex]<br />
<br />
Dirac's notation is fine for dealing with vectors and their duals. However, things quickly become cumbersome when you deal with tensor products. It's not uncommon for one to deal with tensors of rank four and above; in coordinate free notation this would simply be \mathbf{T}(W,X,Y,Z), while in index notation it's just T^{ijkl}. Contrast that with it's representation in Dirac notation:<br />
<br />
\mathbf{T}\to<br />
|W\rangle\otimes|X\rangle\otimes|Y\rangle\otimes|Z\rangle.<br />
<br />
See? It's too cumbersome to bother with. As with all of these kinds of things, notation is just a tool: you pick the one most suited to the job at hand.
