Haag's theorem

Intuitive

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

Concrete

For the best explanation, see the section "How to stop worrying about Haag's theorem" in the book "The Conceptual Framework of Quantum Field Theory" by A. Duncan

Abstract

In particular Haag's theorem, that one cannot consistently define the vacuum in interacting theories, is now considered to have been the wrong way to look at the problem, and largely disappears with considerations of RG flow.A Practical Introduction to Quantum Field Theory by Felix Flicker

Why is it interesting?

According to something called Haagís theorem there appears to be no known consistent formalism within which interacting quantum field theory can be expressed.

p. 115 in "An interpretative introduction to quantum Field theory" by Teller (1995)

FAQ

Why is there no problem in practical QFT calculations?: see https://physics.stackexchange.com/questions/3983/haags-theorem-and-practical-qft-computations