Group averaging, positive definiteness and superselection sectors

Louko, Jorma

doi:10.1088/1742-6596/33/1/013

Cited by 10 publications

(11 citation statements)

References 36 publications

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“…See [13,15,16,17] for comments on this issue. We are concerned here with generic states, and so will not treat the vacuum in detail.…”

Section: B States With Weak Back-reactionmentioning

confidence: 99%

“…[12] showed that this is the case for a 1+1 free scalar toy model and for 3+1 linearized gravitons. While examples (in other contexts) are known for which group averaging is not positive definite [16], these cases are rather singular even at the classical level. Furthermore, when group averaging converges, one can show [21] that it gives the unique physical inner product consistent with the *-algebra of observables on H 0 ; i.e., if it fails to be positive definite, then no renormalized inner product will be positive.…”

Section: A De Sitter Invariant Statesmentioning

confidence: 99%

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A global picture of quantum de Sitter space

Giddings

Marolf

2007

Phys. Rev. D

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Perturbative gravity about a de Sitter background motivates a global picture of quantum dynamics in 'eternal de Sitter space,' the theory of states which are asymptotically de Sitter to both future and past. Eternal de Sitter physics is described by a finite dimensional Hilbert space in which each state is precisely invariant under the full de Sitter group. This resolves a previously-noted tension between de Sitter symmetry and finite entropy. Observables, implications for Boltzmann brains, and Poincaré recurrences are briefly discussed.

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“…See [13,15,16,17] for comments on this issue. We are concerned here with generic states, and so will not treat the vacuum in detail.…”

Section: B States With Weak Back-reactionmentioning

confidence: 99%

Section: A De Sitter Invariant Statesmentioning

confidence: 99%

A global picture of quantum de Sitter space

Giddings

Marolf

2007

Phys. Rev. D

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“…Since group averaging is a technique for taking the action of this observable algebra on H aux and constructing a representation on de Sitter-invariant states, it is clear that the vacuum must be treated separately. See [52,14,53,22,23,24] for more discussion and further examples of this phenomenon.…”

Section: Discussionmentioning

confidence: 99%

Group averaging for de Sitter free fields

Marolf

Morrison

2009

Class. Quantum Grav.

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Perturbative gravity about global de Sitter space is subject to linearizationstability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitter-invariant states except the vacuum, though a new Hilbert space of de Sitter invariant states can be constructed via so-called group-averaging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general N -particle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.

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“…The quantization process will be carried out according to Dirac's approach [39] and employing the so-called group averaging technique [41][42][43][44]. Since this approach does not restrict phase-space variables by means of gauge constraints, the proper-time perspective will be retrieved through the quantization of the proper-time physical variables presented in (11).…”

Section: Proper-time Quantizationmentioning

confidence: 99%

Localization POVMs and intrinsic temporal uncertainty

Taillebois,

Avelar

2020

Preprint

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The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time formalism of single-particle operators. Starting from the premise that physical variables associated to the proper-time gauge have a prominent role in the specification of position, since they do not depend on classical parameters connected to an external observer, we obtain a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper-time. Among the consequences of this result, we emphasize that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.

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Group averaging, positive definiteness and superselection sectors

Cited by 10 publications

References 36 publications

A global picture of quantum de Sitter space

A global picture of quantum de Sitter space

Group averaging for de Sitter free fields

Localization POVMs and intrinsic temporal uncertainty

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