It's often claimed that the Dirac sea is obsolete in quantum field theory. On the other hand, for example, Roman Jackiw argues in this paper that
Once again we must assign physical reality to Dirac’s negative energy sea, because it produces the chiral anomaly, whose effects are experimentally observed, principally in the decay of the neutral pion to two photons, but there are other physical consequences as well.
Moreover, Roger Penrose argues in his book "Road to Reality" (Section 26.5) that there are two "proposals" for the fermionic vacuum state:
- the state $|0 \rangle$ which is "totally devoid of particles", and
- the the Dirac sea vacuum state $|\Sigma\rangle$, "which is completely full of all negative energy electron states but nothing else".
If we use $|0 \rangle$, we have the field expansion $\psi \sim a + b^\dagger$ where $a$ removes a particle and $b$ creates an antiparticle. But if we use $|\Sigma\rangle$, we write the field expansion as $\psi \sim a + b$ where now $b$ removes a field from the Dirac sea which is equivalent to the creation of an antiparticle.
He later concludes (Section 26.5)
the two vacuua that we have been considering namely $|0 \rangle$ (containing no particles and antiparticles) and $|\Sigma\rangle$ (in which all the negative-energy particle states are fulled) can be considered as being, in a sense, effectively equivalent despite the fact that $|0 \rangle$ and $|\Sigma\rangle$ give us different Hilbert spaces. We can regard the difference between the $|\Sigma\rangle$ vacuum and the $|0 \rangle$ vacum as being just a matter of where we draw a line defining the "zero of charge".
This seems closely related to the issue that we find infinity for the ground state energy and the total ground state charge as a result of the commutator relations which is often handled by proposing normal ordering. To quote again Roman Jackiw
Recall that to define a quantum field theory of fermions, it is necessary to fill the negative-energy sea and to renormalize the infinite mass and charge of the filled states to zero. In modern formulations this is achieved by “normal ordering” but for our purposes it is better to remain with the more explicit procedure of subtracting the infinities, i.e. renormalizing them.
So is it indeed valid to use the Dirac sea vacuum in quantum field theory? And if yes, can anyone provide more details or compare the two approaches in more detail?