Progress in Snyder model

Mignemi, Salvatore

doi:10.22323/1.376.0226

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…In the Snyder model (β > 0), space is discrete and time is continuous, whereas in the anti-Snyder model (β < 0), time is discrete and space is continuous. The sub-algebra involving J µν and x µ is isomorphic to the de Sitter/anti-de Sitter algebra, thereby linking the momentum spaces of Snyder/anti-Snyder models geometrically to de Sitter/anti-de Sitter spacetimes [45]. Refining the Snyder model with isotropic parametrizations while maintaining Lorentz/Poincaré symmetry, lead to the same non-commutative relation and different forms of GUP as elaborated in [46,47].…”

Section: Quantum Spacetime: a Necessitymentioning

confidence: 98%

Unbreakable SU(3) Atoms of Vacuum Energy: A Solution for Cosmological Constant Problem

Farag Ali

2024

Preprint

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This paper addresses the cosmological constant problem, a significant discrepancy highlighted by \cite{Weinberg:1988cp} that underlines a fundamental inconsistency between quantum field theory (QFT) and general relativity (GR). QFT examines matter dynamics within Lorentzian spacetime under standard model symmetry, while GR uses Riemannian geometry but adapts it to ensure local Lorentzian behavior in small regions. Despite the experimental successes of both theories, a major challenge exists in theoretical understanding. This letter seeks to clarify this critical misunderstanding. As the universe cools from its hot beginning, the \(SU(3) \times SU(2) \times U(1)\) standard model gauge symmetry evolves. This symmetry breaks to \(SU(3) \times U(1)\) upon cooling at the electroweak scale and ultimately to \(SU(3)\) alone as temperatures approach near-absolute zero kelvin, facilitated by the experimental Meissner effect. This suggests that \(SU(3)\) symmetry forms the foundational "atoms" of vacuum energy. Calculating the number of \(SU(3)\) vacuum atoms across the universe results in a value that perfectly aligns the theoretical predictions with the observed vacuum energy densities, thereby resolving the cosmological constant problem. Since \(SU(3)\) atoms account for the cosmological constant, they must be unbreakable. The third law of thermodynamics, which states that it is impossible to reach absolute zero Kelvin, provides the protection that prevents SU(3) atoms from breaking at zero Kelvin. This reveals the connection between the third law of thermodynamics and the quark confinement. This leads to the \(SU(3)\) atom creating a mass gap within the universe. This solution serves as a symmetric evidence of gauge-gravity duality as well as gravity-superconductor duality.

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Section: Quantum Spacetime: a Necessitymentioning

confidence: 98%

Unbreakable SU(3) Atoms of Vacuum Energy: A Solution for Cosmological Constant Problem

Farag Ali

2024

Preprint

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“…Because this is a quantum-mechanical setting, we will work in the nonrelativistic limit of the Snyder model. 2 Until recently, this limit was usually taken by simply considering the three-dimensional Euclidean version of the model, thus neglecting the role of the time coordinate [27,28,29,30,31]. However, in [5] it was shown that taking explicitly the limit for c → ∞ gives rise to more complicated relations, where a mixing between time and space variables is still present.…”

Section: Introductionmentioning

confidence: 99%

Diffeomorphisms in momentum space: physical implications of different choices of momentum coordinates in the Galilean Snyder model

Gubitosi¹,

Mignemi²

2021

Preprint

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It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms, produce the same physical predictions is still debated. In this work, we focus our attention on a few different momentum spaces that can be associated to the Galilean Snyder noncommutative spacetime model and show that they produce different predictions for the energy spectrum of the harmonic oscillator.

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Diffeomorphisms in Momentum Space: Physical Implications of Different Choices of Momentum Coordinates in the Galilean Snyder Model

Gubitosi

Mignemi

2022

Universe

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Progress in Snyder model

Abstract: We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutaive QFT and discuss the possibility of obtaining a finite theory.

Cited by 3 publications

References 34 publications

Unbreakable SU(3) Atoms of Vacuum Energy: A Solution for Cosmological Constant Problem

Unbreakable SU(3) Atoms of Vacuum Energy: A Solution for Cosmological Constant Problem

Diffeomorphisms in momentum space: physical implications of different choices of momentum coordinates in the Galilean Snyder model

Diffeomorphisms in Momentum Space: Physical Implications of Different Choices of Momentum Coordinates in the Galilean Snyder Model

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