That's not quite what Haag's theorem says. A free field and an interacting field are different things, and one cannot "become" the other, regardless of what Haag's theorem or any other mathematical result says.lindberg said:according to Haag's theorem, a free field cannot become an interacting one?
Wasn't Haag's conclusion extended later to other approaches?PeterDonis said:To someone who is used to the usual way of modeling interacting fields as perturbations of free fields, this seems like a problem; but there are other approaches to quantum field theory, such as the algebraic approach, in which it is not a problem at all.
Given that the whole point of the algebraic approach to QFT is to be able to deal with unitarily inequivalent representations, showing that the algebraic approach leads to unitarily inequivalent representations isn't much of an issue.lindberg said:Wasn't Haag's conclusion extended later to other approaches?
Haag's Theorem is a mathematical proof in quantum field theory that states that it is impossible to construct a self-consistent, interacting quantum field theory with an infinite number of free fields. In other words, it shows that the concept of a completely free field does not exist in nature.
Haag's Theorem is important because it helps us understand the limitations of our current understanding of quantum field theory. It also has implications for the interpretation of quantum mechanics and the nature of reality.
In quantum field theory, a free field is one that does not interact with any other fields. This means that the field's equations of motion are linear and there are no interactions between particles. Free fields are often used as a starting point for constructing more complex theories.
Haag's Theorem tells us that there are fundamental limitations to our understanding of the universe. It suggests that the concept of a completely free field is not applicable to our physical world, and that there must be interactions between fields in order for a theory to be self-consistent.
There are some ways to work around Haag's Theorem, such as using effective field theories or introducing new mathematical techniques. However, these approaches do not fully solve the problem and there is still much research being done to better understand the implications of Haag's Theorem in quantum field theory.