Haag’s Theorem and its Implications for the Foundations of Quantum Field Theory

Earman, John; Fraser, Doreen

doi:10.1007/s10670-005-5814-y

Cited by 73 publications

(59 citation statements)

References 58 publications

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“…Only with the non factual 3+1 splitting of Minkowski space-time and the non factual definition of the global Poincare' generators of an isolated system is it possible define the instantaneous 3-spaces where to give the Cauchy data. In this way, at least at the classical level, it is possible to avoid the Haag theorem [52] preventing the existence of interpolating fields as shown in paper I. 27 For such projectors there is Malament's theorem [48] saying that the requirements of localizability, translation covariance, energy bounded below and microcausality imply that there is no chance that a particle will be detected in any local region.…”

Section: Quantum Field Theorymentioning

confidence: 99%

Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Alba

Crater

Lusanna

2011

Journal of Mathematical Physics

108

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A new formulation of relativistic quantum mechanics is proposed in the framework of the restframe instant form of dynamics with its instantaneous Wigner 3-spaces and with its descrption of the particle world-lines by means of derived non-canonical predictive coordinates. In it we quantize the frozen Jacobi data of the non-local 3-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space h1whose existence is implied by Wigner-covariance. The formalism takes care of the properties of both relativistic bound states and scattering ones. There is a natural solution to the relativistic localization problem. The non-relativistic limit leads to standard quantum mechanics but with a frozen Hamilton-Jacobi description of the center of mass. Due to the non-locality of the Poincare' generators the resulting theory of relativistic entanglement is both kinematically non-local and spatially non-separable, properties absent in the non-relativistic limit.

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Section: Quantum Field Theorymentioning

confidence: 99%

Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Alba

Crater

Lusanna

2011

Journal of Mathematical Physics

108

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“…Indeed, Fraser (2008) convincingly argues that the Fock space representation is in general and strictly speaking only available for free, non-interacting QFT systems; central to her argument is the fact that free and interacting QFT systems involve unitarily inequivalent representations (this can also be seen as a consequence of Haag's theorem, see Earman and Fraser 2006). So, there is in general no Fock space representation for a QFT with interactions-that is, a realistic QFT.…”

Section: Equivalent Difficulties For Particle and Field Primitive Ontmentioning

confidence: 99%

Primitive ontology and quantum field theory

Lam

2015

Euro Jnl Phil Sci

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Primitive ontology is a recently much discussed approach to the ontology of quantum theory according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. This paper critically discusses the primitive ontologies that have been suggested within the Bohmian approach to quantum field theory in the light of the existence of unitarily inequivalent representations. These primitive ontologies rely either on a Fock space representation or a wave functional representation, which are strictly speaking unambiguously available only for free systems in flat spacetime. As a consequence, it is argued that they do not constitute fundamental ontologies for quantum field theory, in contrast to the case of the Bohmian approach to quantum mechanics.

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“…This has to be contrasted with QED, where we must consider only the S matrix between IN and OUT free fields and not the interpolating fields due to the Haag theorem, saying that the interaction picture does not exist [16,17] and that there is no unitary transformation from the asymptotic IN and OUT states of the radiation field to interpolating states of the general (non radiation) electro-magnetic field. See the end of Section III.…”

Section: The Need Of This Formulation Comes From At Least Two Directimentioning

confidence: 99%

“…B) As shown in Refs. [11], where the Møller world-tube was introduced in connection with the Møller center of energy R µ (τ ), an extended rotating relativistic isolated system with the material radius smaller than its intrinsic radius ρ one has: i) its peripheral rotation velocity can exceed the velocity of light; ii) its classical energy density cannot be positive definite everywhere in every frame 17 . Therefore the Møller radius ρ is also a remnant of the energy conditions of general relativity in flat Minkowski space-time [7].…”

Section: F the Møller Radius And The Comparison With Other Approachementioning

confidence: 99%

Towards relativistic atomic physics. Part 1. The rest-frame instant form of dynamics and a canonical transformation for a system of charged particles plus the electro-magnetic field

2010

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A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids) admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. The restriction to the inertial rest frame, centered on the inertial observer having the Fokker-Pryce center-of-inertia world-line, and the study of relativistic collective variables replacing the non-relativistic center of mass lead to the description of the isolated system as a decoupled globally-defined non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass M and the rest spin S of the system) and an external realization of the Poincare' group. M c and S are the energy and angular momentum of a unfaithful internal realization of the Poincare' group built with the energy-momentum tensor of the system and acting inside the instantaneous Wigner 3-spaces where all the 3-vectors are Wigner covariant. The vanishing of the internal 3-momentum and of the internal Lorentz boosts eliminate the internal 3-center of mass inside the Wigner 3-spaces, so that at the end the isolated system is described only by Wigner-covariant canonical internal relative variables.Then an isolated system of positive-energy charged scalar articles with mutual Coulomb interaction plus a transverse electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The external and internal realizations of the Poincare' algebra in the rest-frame instant form of dynamics are found. This allows one to define explicitly the rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) for this isolated system. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting (the internal Poincare' generators are a direct sum of the two components) and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem, at least at the classical level.

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Haag’s Theorem and its Implications for the Foundations of Quantum Field Theory

Cited by 73 publications

References 58 publications

Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Primitive ontology and quantum field theory

Towards relativistic atomic physics. Part 1. The rest-frame instant form of dynamics and a canonical transformation for a system of charged particles plus the electro-magnetic field

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