Related papers: Haag as a How-To Theorem
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are…
Haag's theorem cries out for explanation and critical assessment: it sounds the alarm that something is (perhaps) not right in one of the standard way of constructing interacting fields to be used in generating predictions for scattering…
We revisit the implications of Haag's theorem in the light of the renormalization group. There is still some lack of discussion in the literature about the possible impact of the theorem on the standard (as opposite of axiomatic) quantum…
Haag's theorem was extended to noncommutative quantum field theory in a general case when time does not commute with spatial variables. It was proven that if S-matrix is equal to unity in one of two theories related by unitary…
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on…
Haag's theorem states that if a quantum field theory is Lorentz invariant and irreducible, there is no interaction picture. But if we construct quantum field theory on a discrete lattice spacetime, its representation will be reducible and…
Generalized Haag's theorem has been proved in S O (1, k) invariant quantum field theory. Apart from the above mentioned k+1 variables there can be arbitrary number of additional coordinates including noncommutative ones in the theory. New…
Haag's theorem has shown that the transformation between interacting and free field operators in a reasonable quantum field theory cannot be unitary. Here, the original requirement of unitarity is revisited from a physical point of view to…
Haag's theorem is extended to the case of regular representations of the canonical commutation relations in a non-degenerate indefinite inner product space.
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
One of the most important results of the axiomatic quantum field theory - generalized Haag's theorem - is proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3)…
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the…
It is demonstrated that the "dressed particle" approach to relativistic local quantum field theories does not contradict Haag's theorem. On the contrary, "dressing" is the way to overcome the difficulties revealed by Haag's theorem.
It is argued that the severe consequences of Haag's inconsistency theorem for relativistic quantum field theories can be successfully evaded in the direct-action approach. Some recent favorable comments of John Wheeler, often mistakenly…
Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important…
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption…
Following P. A. M. Dirac's critique in ``Lectures on Quantum Field Theory'' of the usual formalism, I will discuss the role of the time parameter to solve R. Haag's no-go theorem on the non-equivalence of the conventional Schr\"odinger…
Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with…
Classical results of the axiomatic quantum field theory, namely the irreducibility of the set of field operators, Reeh and Schlieder's theorems and generalized Haag's theorem, are proven in $SO(1,1)$ invariant quantum field theory, of which…
The Fock-Hilbert space generated by a single-particle interaction-free Wightman field is augmented by introducing non-trivial multi-particle (that is, multi-point, multilinear) quantum fields, which is justified insofar as Haag's theorem…