Uniqueness of inverse scattering problem in local quantum physics

Schroer, Bert

doi:10.1016/s0003-4916(03)00114-3

Cited by 14 publications

(34 citation statements)

References 23 publications

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“…Whereas theories involving the first two families have generating pointlike localized field strengths, there are no pointlike covariant generators within the last family; rather the sharpest localized generators in that case are semiinfinite strings localized along the spacelike half-line x + R + e, where x is the starting point of the string and e is the spacelike direction in which it extends to spacelike infinity. Their localization shows up in their commutation relation which we presented in (15).…”

Section: A Turn With Grave Consequencesmentioning

confidence: 83%

“…The result is the formula for a one point expectation value in a thermal KMS state with respect to the Lorentz boost Hamiltonian K at temperature 2π. As we will see in a moment, the modular relation (7) in the Wigner one-particle setting is the pre-stage for the crossing relation as well as an associated KMS property in an interacting QFT 15 . Before we get to that point we first need to generalize the above derivation to all positive energy representations and then explain how to get to the subwedge modular localization for compact regions.…”

Section: An Anthology Of the Crisis In The Foundations Of Particle Phmentioning

confidence: 92%

“…attempts to implement them by "hand" are then delegated to the (successful) proof of asymptotic convergence for large times. Assuming that crossing holds for formfactors (a reasonable extrapolation of what has been proven in QFT) though one cannot show the existence of an associated QFT, at least its uniqueness can be established [15].…”

Section: A Turn With Grave Consequencesmentioning

confidence: 98%

“…The connection between off-shell local quantum physics and the on-shell S-matrix also shows the futility to invert this connection via scattering theory by hand (this does not prevent string theorist to contemplate such off-shell extrapolations). An S-matrix fulfilling the crossing property can however be shown to admit only one inverse scattering solution 11 if one assumes that the formfactors of the local quantum theory are also bound together by crossing [15]. Unfortunately such uniqueness arguments have, apart from the family of two-dimensional factorizing models, not led to concrete constructions.…”

Section: An Anthology Of the Crisis In The Foundations Of Particle Phmentioning

confidence: 99%

“…The N-G string is not even a decomposable string in the sense of a pointlike field spread over a infinitely thin tube. Indecomposable stringlike localized objects occur in Wigner's representation theory but they have nothing in common with the pointlike localized objects of string theory presented in (15).…”

Section: A Turn With Grave Consequencesmentioning

confidence: 99%

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String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

Schroer

2008

Int. J. Mod. Phys. D

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This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of string theory within the broader context of six decades of failed attempts at an autonomous S matrix approach to particle theory. The central message, contained in Secs. 5 and 6, is that string theory is not what its name suggests, namely a theory of objects in space–time whose localization is string-instead of pointlike. Contrary to popular opinion, the oscillators corresponding to the Fourier models of a quantum-mechanical string do not become embedded in space–time and neither does the "range space" of a chiral conformal QFT acquire the interpretation of stringlike-localized quantum matter. Rather, string theory represents a solution to a problem which enjoyed some popularity in the 1960s: find a principle which, similar to the SO (4,2) group in the case of the hydrogen spectrum, determines an infinite component wave function with a (realistic) mass/spin spectrum. Instead of the group theory used in the old failed attempts, it creates this mass/spin spectrum by combining an internal oscillator quantum mechanics with a pointlike-localized quantum-field-theoretic object, i.e. the mass/spin tower "sits" over one point and does not arise from a wiggling string in space–time. The widespread acceptance of a theory whose interpretation has been based on metaphoric reasoning had a corroding influence on particle theory, a point which will be illustrated in the last section with some remarks of a more sociological nature. These remarks also lend additional support to observations on connections between the discourse in particle physics and the present Zeitgeist of the post–Cold War period that are made in the introduction.

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Section: A Turn With Grave Consequencesmentioning

confidence: 83%

Section: An Anthology Of the Crisis In The Foundations Of Particle Phmentioning

confidence: 92%

Section: A Turn With Grave Consequencesmentioning

confidence: 98%

Section: An Anthology Of the Crisis In The Foundations Of Particle Phmentioning

confidence: 99%

Section: A Turn With Grave Consequencesmentioning

confidence: 99%

See 3 more Smart Citations

String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

Schroer

2008

Int. J. Mod. Phys. D

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Quantenfeldtheorie und topologie

Schroer

Einstein Symposion Berlin

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A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

Schroer

2010

Found Phys

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The crossing property is perhaps the most subtle aspect of the particlefield relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization-and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from "modular localization" including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where "dynamic" means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4, 2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d = 9 + 1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. Dedicated to Ivan Todorov on the occasion of his 75th birthday. B. Schroer ( ) CBPF, Rua Dr. Xavier Sigaud 150,

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Uniqueness of inverse scattering problem in local quantum physics

Cited by 14 publications

References 23 publications

String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

Quantenfeldtheorie und topologie

A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

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