Where Infinite Spin Particles are Localizable

Longo, Roberto; Morinelli, Vincenzo; Rehren, Karl-Henning

doi:10.1007/s00220-015-2475-9

Cited by 33 publications

(41 citation statements)

References 30 publications

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“…The recent observation that Wigner's infinite spin representation class admits no compact causal localization [4] and that its tightest localized quantum fields "live" on semi-infinite strings (space-like rays) S(x, e) = x + R + e, e 2 = −1 [5] led to several new fundamental problems concerning the foundational properties of quantum fields. Besides the obvious question concerning possible physical manifestations of this new form of matter one could also ask whether a better understanding of the interplay between positivity and causal localization could favor the use of string-localized (sl) fields in a positivity-maintaining formulation of interactions involving finite higher spin particles.…”

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

“…These considerations were strengthened in [11]. A rigorous proof which excludes the possibility of finding compact localized subalgebras (generated by test-function-smeared pl fields) was finally presented in a seminal paper by Longo et al [4].…”

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

“…But the recent gain of knowledge from modular localization regarding attempts to unite WS with normal matter under the conceptual roof of AQFT in [4], as well as new insights coming from preliminary perturbative studies of couplings involving string-local fields [17,18], led to a revision of these ideas.…”

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

“…In [4] it was shown that the attempt to unite normal matter (matter as we know it) together with WS in a nontrivial way 3 under the conceptual roof of algebraic QFT (AQFT) leads to an unexpected loss of the so-called "Reeh-Schlieder property" for compact localized observable algebra. The R-S property states that the set of state vectors obtained by the application of operators from a compact localized subalgebra of local observables to the vacuum is "total" in the vacuum Hilbert space [13].…”

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

“…This leaves the conclusion that, apart from gravitational backreaction which require the solution of additional renormalization problems of the stress-energy tensor 4 (the substitute for the vacuum-based Wick-product [12]), WS cannot interact with normal matter in a way which complies with the causal localization structure of QFT. In mathematical terminology, WS matter tensor-factorizes with normal matter and the standard properties (including the ReehSchlieder cyclic action of local subalgebras on the vacuum vector [13]) hold only in the tensor factor of normal matter.…”

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

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Wigner’s infinite spin representations and inert matter

Schroer

2017

Eur. Phys. J. C

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Positive energy ray representations of the Poincaré group are naturally subdivided into three classes according to their mass and spin content: m > 0, m = 0 finite helicity and m = 0 infinite spin. For a long time the localization properties of the massless infinite spin class remained unknown, until it became clear that such matter does not permit compact spacetime localization and its generating covariant fields are localized on semi-infinite spacelike strings. Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this also could happen for finite spin s > 1 fields. This raises the question of a possible connection between inert matter and dark matter. Wigner's infinite spin representation and string-localizationWigner's famous 1939 theory of unitary representations of the Poincaré group P was the first systematic and successful attempt to classify relativistic particles according to the intrinsic principles of relativistic quantum theory [1]. As we know nowadays, his massive and massless spin/helicity class of positive energy ray representations of P does not only cover all known particles, but their "covariantization" [2] leads also to a complete description of all covariant pointlocal (pl) free fields. For each covariant Lorentz transformation property compatible with physical spin or helicity there exists a pl field.It is not necessary that these free fields permit a characterization as Euler-Lagrange fields; in fact the attempt to describe higher spin fields in this way and pass to quantum fields by canonical quantization or use other ways to Dedicated to the memory of Robert Schrader. a e-mail: schroer@zedat.fu-berlin.de start from a classical field creates problems of their own. On the other hand the construction of free fields starting from Wigner's representation theory does not require one to rely on any "quantization parallelism" to classical structures.The idea that a more fundamental theory should not rely on structural properties of a less basic one can also be upheld in the presence of interactions. Defining a first order Lorentz invariant interaction densities in terms of products of free fields and using the Epstein-Glaser [3] formulation of renormalization theory permits a perturbative cutoff-and regularization-free higher order inductive implementation of the causal localization principle in a positivity-obeying Wigner-Fock Hilbert space without a reference to the classical field formalism. Renormalizable theories in this setting are those for which this higher order induction increases the model-defining first order parameters by an at most finite number of "counter term" parameters. When higher spin s ≥ 1 fields participate in the interaction there are no positivity-obeying renormalizable couplings. The traditional way out has been to skip positivity in the calculations and save it by restricting the result. A total abandonment would have...

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Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

Section: Wigner's Infinite Spin Representation and String-localizationmentioning

confidence: 99%

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Wigner’s infinite spin representations and inert matter

Schroer

2017

Eur. Phys. J. C

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The D-CTC Condition in Quantum Field Theory

Verch

2020

Progress and Visions in Quantum Theory in View of Gravity

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A condition proposed by David Deutsch to describe analogues of processes in the presence of closed timelike curves (D-CTC condition) in bipartite quantum systems is investigated within the framework of local relativistic quantum field theory. The main result is that in relativistic quantum field theory on spacetimes where closed timelike curves are absent, the D-CTC condition can nevertheless be fulfilled to arbitrary precision, under very general, model-independent conditions. Therefore, the D-CTC condition should not be taken as characteristic for quantum processes in the presence of closed timelike curves in the sense of general relativity. This report is a very condensed extract of the publication [35]. A new result showing that the D-CTC condition can be approximately fulfilled by entangled states is also presented.

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