The Geometry of Noncommutative Spacetimes

Eckstein, Michał

doi:10.3390/universe3010025

Cited by 6 publications

(4 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From a purely mathematical standpoint, apart from various problems that have been already pointed out in the main text, such as the extension of the characterization of causal structures to nondiscrete groupoids or the relation between nonstrict causal categories and general Kadison–Singer algebras, the relation between causal structures, Kadison–Singer algebras, and von Neumann algebras associated with groupoids is a new and promising path of research that will be pursued by relating it to previous attempts to tamper the problem of causality in quantum systems by using noncommutative geometrical ideas (see, for instance, [ 48 , 49 , 50 ]).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Causality in Schwinger’s Picture of Quantum Mechanics

Ciaglia

Cosmo

Ibort

et al. 2022

Entropy

View full text Add to dashboard Cite

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Causality in Schwinger’s Picture of Quantum Mechanics

Ciaglia

Cosmo

Ibort

et al. 2022

Entropy

View full text Add to dashboard Cite

show abstract

“…Four-dimensional NC relativistic space (or relativistic fuzzy space) with conformal symmetry will be of our interest in this paper. There have not been many explicit realizations of this issue ( [18]): the idea of Connes's almost non-commutative geometry ( [19]), κ-deformed Minkowski space ( [20], [21]) or direct efforts of adding gravitational fields to NC spaces ( [22]). All are classical and lack direct ability to be quantized.…”

Section: Motivation and Introductionmentioning

confidence: 99%

Some oscillatory representations of fuzzy conformal group SU(2,2) with positive energy

Beznák,

Prešnajder

2020

Preprint

View full text Add to dashboard Cite

We construct the relativistic fuzzy space as a non-commutative algebra of functions with purely structural and abstract coordinates being the creaction and annihilation (C/A) operators acting on a Hilbert space HF . Using these oscillators, we represent the conformal algebra su(2, 2) (containing the operators describing physical observables, that generate boosts, rotations, spatial and conformal translations, and dilatation) by operators acting on such functions and reconstruct an auxiliary Hilbert space HA to describe this action. We then analyze states on such space and prove them to be boost-invariant. Eventually, we construct two classes of irreducible representations of su(2, 2) algebra with half-integer dimension d ([1]): (i) the classical fuzzy massless fields as a doubleton representation of the su(2, 2) constructed from one set of C/A operators in fundamental or unitary inequivalent dual representation and (ii) classical fuzzy massive fields as a direct product of two doubleton representations constructed from two sets of C/A operators that are in the fundamental and dual representation of the algebra respectively.

show abstract

“…From these facts emerges the possibility that GR may be modified. Several modified gravity theories have been developed, such as F(R) gravity [4,5], bumblebee model [6], Chern-Simons gravity [7], Brans-Dicke theory [8], F(R,T) gravity [9], higher derivative gravity [10], hybrid metric-Palatini gravity [11], conformally coupled general relativity [12], bigravity [13], non-commutative space-times [14], de Sitter Horndeski models [15], gravity with Lorentz violation [16], orbital effects of Lorentz-violating gravitomagnetism [17], Chameleonic theories [18], generalized f(R,Φ, X) gravity [19], supergravity [20], arctan-gravity [21], f(T) gravity [22,23], among others.…”

Section: Introductionmentioning

confidence: 99%

On causality violation in Lyra Geometry

Jesus

Santos

2018

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

In this paper the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the Gödel and Gödeltype metric are consistent with this non-Riemannian geometry. A non-trivial solution for Gödel universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal solutions are discussed.

show abstract

The Geometry of Noncommutative Spacetimes

Cited by 6 publications

References 73 publications

Causality in Schwinger’s Picture of Quantum Mechanics

Causality in Schwinger’s Picture of Quantum Mechanics

Some oscillatory representations of fuzzy conformal group SU(2,2) with positive energy

On causality violation in Lyra Geometry

Contact Info

Product

Resources

About