Quantum Spacetime and Algebraic Quantum Field Theory

Bahns, Dorothea; Doplicher, Sergio; Morsella, Gerardo; Piacitelli, Gherardo

doi:10.1007/978-3-319-21353-8_7

Cited by 27 publications

(49 citation statements)

References 35 publications

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“…To this purpose, we may think to a physical situation near the classical big bang singularity where spacetime quantum fluctuations together with interactions among particles [9,10] can be studied with a simplified model with our test particle interacting with a delta potential. In this framework, as will be shown in this paper, Planckian fluctuations due to a non commutative spacetime [11,12,13,14,15,16] give a negative contributon to the energy content of the universe. The above negative contribution can, in the present model, be obtained in terms of an attractive delta interactions, experienced by our test particle.…”

Section: Introductionmentioning

confidence: 79%

“…This picture changes drastically if a(t) does not follow the classical trajectory, this is possible when quantum gravity planckian fluctuations come in action at Planckian scales. This can be physically possible by supposing a quantum spacetime at Planckian scale [11,12,13,14,15,16]. In particular in [11] a quantum spacetime model has been obtained starting from physically motivated uncertainity relations (STUR), finding commutation relations among spacetime coordinates q µ .…”

Section: An Application: Testing a Primordial Friedmann Universe On Amentioning

confidence: 99%

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The 3D Perturbed Schrödinger Hamiltonian in a Friedmann Flat Spacetime Testing the Primordial Universe in a Non Commutative Spacetime

Fassari

Rinaldi

Viaggiu

2019

Math Phys Anal Geom

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In this paper we adapt the mathematical machinery presented in [1] to get, by means of the Laplace-Beltrami operator, the discrete spectrum of the Hamiltonian of the Schrödinger operator perturbed by an actractive 3D delta interaction in a Friedmann flat universe. In particular, as a consequence of the treatment in [1] suitable for a Minkowski spacetime, the discrete spectrum of the ground state and the first exited state in the above mentioned cosmic framework can be regained. Thus, the coupling constant λ must be choosen as a function of the cosmic comooving time t as λ/a 2 (t), with λ be the one of the static Hamiltonian studied in [1]. In this way we can introduce a time * sifassari@gmail.com † f.rinaldi@unimarconi.it ‡ s.viaggiu@unimarconi.it and viaggiu@axp.mat.uniroma2.it dependent delta interaction which is relevant in a primordial universe, where a(t) → 0 and becomes negligible at late times, with a(t) >> 1. We investigate, with the so obtained model, quantum effects provided by point interactions in a strong gravitational regime near the big bang. In particular, as a physically interesting application, we present a method to depict, in a semi-classical approximation, a test particle in a (non commutative) quantum spacetime where, thanks to Planckian effects, the initial classical singularity disappears and as a consequnce a ground state with negative energy emerges. Conversely, in a scenario where the scale factor a(t) follows the classical trajectory, this ground state is instable and thus physically cannot be carried out.

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Section: Introductionmentioning

confidence: 79%

Section: An Application: Testing a Primordial Friedmann Universe On Amentioning

confidence: 99%

The 3D Perturbed Schrödinger Hamiltonian in a Friedmann Flat Spacetime Testing the Primordial Universe in a Non Commutative Spacetime

Fassari

Rinaldi

Viaggiu

2019

Math Phys Anal Geom

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“…The model of QST adopted here is suggested by the Principle of Gravitational Stability against localization of events [8], [1]. This principle implies Spacetime Uncertainty Relations…”

Section: The Magnetic Moment Of a Neutral Scalar Field Induced By Quamentioning

confidence: 99%

“…The noncommutative C* algebra E of Quantum Spacetime can be associated to the above relations, by a procedure [7,1] which applies to more general cases.…”

Section: The Magnetic Moment Of a Neutral Scalar Field Induced By Quamentioning

confidence: 99%

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Dark matter and weak signals of quantum spacetime

et al. 2017

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A U(1) gauge theory turns, on physically motivated models of Quantum Spacetime, into a U(∞) gauge theory, hence free classical electrodynamics is no longer free and neutral fields may have electromagnetic interactions. We discuss the last point for scalar fields, possibly describing dark matter; we have in mind the gravitational collapse of binary systems or future applications to self gravitating Bose-Einstein condensates as possible sources of evidence of quantum gravitational phenomena. The effects so far considered, however, seem too faint to be detectable at present.

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Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections

Albeverio

2022

When Form Becomes Substance

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Quantum Spacetime and Algebraic Quantum Field Theory

Cited by 27 publications

References 35 publications

The 3D Perturbed Schrödinger Hamiltonian in a Friedmann Flat Spacetime Testing the Primordial Universe in a Non Commutative Spacetime

The 3D Perturbed Schrödinger Hamiltonian in a Friedmann Flat Spacetime Testing the Primordial Universe in a Non Commutative Spacetime

Dark matter and weak signals of quantum spacetime

Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections

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