Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Doplicher, Sergio; Morsella, Gerardo; Pinamonti, Nicola

doi:10.1007/s00220-020-03775-4

Cited by 3 publications

(12 citation statements)

References 28 publications

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“…More precisely, analyzing the Yang-Feldman equation with interaction term defined through the QWP, we show in Section 2 below that the interacting field vanishes at first order in perturbation theory in the limit of large Planck length. Moreover, as discussed in Section 3, the same holds, at all orders in perturbation theory, for the interacting observables defined using the adaptation, developed in [9], of the perturbative approach to Algebraic Quantum Field Theory (pAQFT) of [6].…”

Section: Introductionmentioning

confidence: 90%

“…Following [7] and the discussion presented in Section 2, this limit correspond to an early time limit in a cosmological scenario. A convenient framework in which this limit can be controlled at all orders in perturbation theory is the one developed in [9] adapting to QFT on QST the framework of pAQFT. To make the paper reasonably self-contained, we summarize below the main definitions and results of [9], to which we refer the interested reader for more details and proofs.…”

Section: Limits For Large λ P At All Orders In Perturbation Theorymentioning

confidence: 99%

“…A convenient framework in which this limit can be controlled at all orders in perturbation theory is the one developed in [9] adapting to QFT on QST the framework of pAQFT. To make the paper reasonably self-contained, we summarize below the main definitions and results of [9], to which we refer the interested reader for more details and proofs. To simplify the notation, from now on we denote the Planck length just by λ.…”

Section: Limits For Large λ P At All Orders In Perturbation Theorymentioning

confidence: 99%

“…The • T λ product is then used in [9] to define the (infrared cutoff) S matrix corresponding to the interaction (3.2) as…”

Section: Proposition 31 For Every a B ∈ A The Following Limits Holdmentioning

confidence: 99%

“…In [9] an effective description of the interaction in a quantum spacetime has been developed using an effective interaction Lagrangian which is different from the one in [3], but which is equivalent to it in the adiabatic limit, namely after integration of the effective Lagrangian density over the full spacetime. This new interaction Lagrangian is obtained by replacing in the classical Lagrangian density the field operators at a point x by fields at a quantum point described by states optimally localized around x.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

Doplicher

Morsella

Pinamonti

2020

Math Phys Anal Geom

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As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

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Section: Introductionmentioning

confidence: 90%

Section: Limits For Large λ P At All Orders In Perturbation Theorymentioning

confidence: 99%

Section: Limits For Large λ P At All Orders In Perturbation Theorymentioning

confidence: 99%

“…The • T λ product is then used in [9] to define the (infrared cutoff) S matrix corresponding to the interaction (3.2) as…”

Section: Proposition 31 For Every a B ∈ A The Following Limits Holdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

Doplicher

Morsella

Pinamonti

2020

Math Phys Anal Geom

Self Cite

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Renormalization on the DFR quantum spacetime

López,

Reyes-Lega

2024

Rev. Math. Phys.

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An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the nonlocal kernel that codifies the effects of non-commutativity is analyzed using the tools of microlocal analysis.

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Renormalization on the DFR Quantum Spacetime

López¹,

Reyes-Lega²

2023

Preprint

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An approach to renormalization of scalar fields on the Doplicher-Fredenhagen-Roberts (DFR) quantum spacetime is presented. The effective non-local theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the non-local kernel that codifies the effects of noncommutativity is analyzed using the tools of microlocal analysis.

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Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

Cited by 3 publications

References 28 publications

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

Renormalization on the DFR quantum spacetime

Renormalization on the DFR Quantum Spacetime

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