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When studying the QFT, one considers the vacuum state when the field is not excited and therefore no particles are present.

Now for the matter fields this makes sense to me.

But what about the radiation field?

Suppose we have an arbitrary small volume of space in the universe without any matter particles inside of it. An empty volume of space.

But can we say that there are not any photons inside this empty spatial volume?

I mean regardless of where we pick the empty volume in the universe there is some radiation coming to that volume from some galaxy source.

Then what is actually the difference between an empty (of matter) space and the vacuum that is talked about in the QFT.

I suppose by QFT vacuum we actually mean even there is no excitation of the electromagnetic field and therefore no photons.

But can we have any volume of space at any time through which a photon doesn't pass?

VVM
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I think there are actually three concepts of vacuum that are being confused here

  • The "free vacuum" is the one where there are no excitations. That means no matter particles, no photons, it is the 'nothing' state.
  • The "interacting vacuum" is the actual ground state (lowest energy state) of a quantum field theory, and it is (perhaps surprisingly) not the same thing as the free vacuum, colloquially we say there are particle-antiparticles populating the vacuum.
  • This is not standard terminology, but I believe you are also mentioning the "cosmic vacuum", that is to say, what we think of as empty space, if I were to travel to outer space in a rocket. I'm basing this off this quote in your question "there is some radiation coming to that volume from some galaxy source". This 'outer space' is, as you've observed, not really empty at all, in fact the Cosmic Microwave Background photons are flying around in outer space, heating it to a temperature of about 3 Kelvin.

These three vacuums are different. In Quantum Field Theory, most often you will be working with the first two, and not dealing with thermal effects.

QCD_IS_GOOD
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