Related papers: Haag's theorem in renormalised quantum field theor…
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…
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…
Haag's theorem is a classic no-go theorem. It rigorously demonstrates there is a logical problem with the interaction picture (IP), one of the most widely used modeling tools in quantum field theory (QFT). The significance of the theorem…
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…
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)…
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…
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…
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…
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…
Haag's theorem is extended to the case of regular representations of the canonical commutation relations in a non-degenerate indefinite inner product space.
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…
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…
We define quantum field theory by taking the Lagrangian action to be given as a sequence of mathematically well-defined functionals written in terms of operator fields fulfilling given \hbox{local} commutation relations. The renormalized…
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…
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…
In 1952, L\'{e}on van Hove published an article, in French, with the title ``Les difficult\'{e}s de divergences pour um mod\`{e}le particulier de champ quantifi\'{e}''. The article is frequently cited in relation to Haag's theorem and to…
The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…
The Hamiltonian approach to the quantum field theory is considered. Since there are additional difficulties such as the Haag theorem and Stueckelberg divergences, renormalization of the time-dependent dynamical quantum field theory is much…
We dwell upon certain points concerning the meaning of quantum field theory, among these the problems with the perturbative approach, and the question raised by tHooft of the existence of the theory in a well defined mathematical sense, as…
The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of generalized functions adapted to nonlinear operations. The…