From Wikipedia: [The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons. The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, well before its experimental discovery in 1932.]
and:
[Dirac's idea is completely correct in the context of solid state physics, where the valence band in a solid can be regarded as a "sea" of electrons. Holes in this sea indeed occur, and are extremely important for understanding the effects of semiconductors, though they are never referred to as "positrons". Unlike in particle physics, there is an underlying positive charge — the charge of the ionic lattice — that cancels out the electric charge of the sea.]
It always confused me to think of holes as positive charge carriers in semi-conductors as not being real: real electrons move from one lattice-position to another lattice-position, which effectively looks like a positive hole in the lattice that is moving in the other direction, but in reality a real electron moves, the hole is kind of an "illusion".
On the other hand the positrons are always introduced as real hard-core particles.
The quotes from the Wikipedia article make me unsure: how should I look upon these phenomena?
Edit: holes in a Dirac sea give rise to real pos. entities in one case and to unreal pos. entities in another - how can we distinguish, is it a matter of formalism?
Answer
I want to come back to this answer in a bit and expand a bit more, but it seems to me that the notion that you are reaching for is that of quasiparticles, and I want to argue that these might be best understood in the context of effective field theories.
Roughly: the electrons and holes in solid state physics are not actually necessarily true single particles, but actually collective excitations of the material (you can think of an electron quasiparticle as being an electron plus some minor deformation of the underlying lattice plus effects due to interactions with other electrons; the picture for holes is that of an empty electron quasiparticle state).
However, the same is true for electrons and positrons in vacuum (though the energy scales are much different)! The mass of the electron has contributions from a cloud of virtual electron-positron pairs (this is an effect called mass renormalization).
This is a bit confusing -- it turns out that e.g. talking about an electron as a single particle that doesn't interact with itself is a classical notion that breaks down when quantum field theory comes into the picture.
Indeed, quantum field theories (i.e. the best physical pictures that we currently have) are actually agnostic in a certain strong sense as to whether an electron is a single particle, or a particle surrounded by a cloud, or whether a hole is a true particle or a quasiparticle, etc. What do I mean by this? Well, the mathematical models that currently describe the systems best do not talk about particles at all, they talk about excitations in quantum fields, and for interacting quantum fields, it turns out that the coupling constants that go into the Lagrangians for these field theories will get (in general divergent!) corrections from self-interactions. Luckily, we now understand that this is not something to worry about -- there's a technique called "renormalization" which fixes the mathematical divergences, and there's a philosophy of "effective field theories" which explains how to think about these cancellations. Roughly speaking, depending on what energy scale you want to work in, you might interpret the electron as being a single particle, or a fuzzy cloud, but with regards to calculating measurable quantities, it doesn't really matter. For a better take on this, I like the first few sections of Howard Georgi's review "Effective field theory".
Sorry if this doesn't make much sense at the moment. I hope I've given you a few key words to look up. Perhaps someone who understands all this a bit better can come by and explain it in easier terms, or I'll come back and edit it in a few days.
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