Noncommutative spacetimes are a proposed effective description of the low-energy regime of Quantum Gravity. Defining the microcausality relations of a scalar quantum field theory on the κ-Minkowski ...noncommutative spacetime allows us to define for the first time a notion of light-cone in a quantum spacetime. This allows us to reach two conclusions. First, the majority of the literature on κ-Minkowski suggests that this spacetime allows superluminal propagation of particles. The structure of the light-cone we introduced allows to rule this out, thereby excluding the possibility of constraining the relevant models with observations of in-vacuo dispersion of Gamma Ray Burst photons. Second, we are able to reject a claim made in Neves et al. (2010) 33, according to which the light-cone of the κ-Minkowski spacetime has a ‘blurry’ region of Planck-length thickness, independently of the distance of the two events considered. Such an effect would be hopeless to measure. Our analysis reveals that the thickness of the region where the notion of timelike and spacelike separations blurs grows like the square root of the distance. This magnifies the effect, e.g. in the case of cosmological distances, by 30 orders of magnitude.
Fuzzy worldlines with κ-Poincaré symmetries Ballesteros, Angel; Gubitosi, Giulia; Gutierrez-Sagredo, Ivan ...
The journal of high energy physics,
12/2021, Letnik:
2021, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
A novel approach to study the properties of models with quantum-deformed relativistic symmetries relies on a noncommutative space of worldlines rather than the usual noncommutative ...spacetime. In this setting, spacetime can be reconstructed as the set of events, that are identified as the crossing of different worldlines. We lay down the basis for this construction for the
κ
-Poincaré model, analyzing the fuzzy properties of
κ
-deformed time-like worldlines and the resulting fuzziness of the reconstructed events.
In this work we study the deformations into Lie bialgebras of the three relativistic Lie algebras: de Sitter, Anti-de Sitter and Poincaré, which describe the symmetries of the three maximally ...symmetric spacetimes. These algebras represent the centerpiece of the kinematics of special relativity (and its analogue in (Anti-)de Sitter spacetime), and provide the simplest framework to build physical models in which inertial observers are equivalent. Such a property can be expected to be preserved by Quantum Gravity, a theory which should build a length/energy scale into the microscopic structure of spacetime. Quantum groups, and their infinitesimal version ‘Lie bialgebras’, allow to encode such a scale into a noncommutativity of the algebra of functions over the group (and over spacetime, when the group acts on a homogeneous space). In 2+1 dimensions we have evidence that the vacuum state of Quantum Gravity is one such ‘noncommutative spacetime’ whose symmetries are described by a Lie bialgebra. It is then of great interest to study the possible Lie bialgebra deformations of the relativistic Lie algebras. In this paper, we develop a characterization of such deformations in 2, 3 and 4 spacetime dimensions motivated by physical requirements based on dimensional analysis, on various degrees of ‘manifest isotropy’ (which implies that certain symmetries, i.e. Lorentz transformations or rotations, are ‘more classical’), and on discrete symmetries like P and T. On top of a series of new results in 3 and 4 dimensions, we find a no-go theorem for the Lie bialgebras in 4 dimensions, which singles out the well-known ‘κ-deformation’ as the only one that depends on the first power of the Planck length, or, alternatively, that possesses ‘manifest’ spatial isotropy.
A useful concept in the development of physical models on the κ-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum ...space geometries have been identified. Some are associated to a different assumption regarding the signature of spacetime (i.e. Lorentzian vs. Euclidean), but there are inequivalent momentum spaces that can be associated to the same signature and even the same group of symmetries. Moreover, in the literature there are two approaches to the definition of these momentum spaces, one based on the right- (or left-)invariant metrics on the Lie group generated by the κ-Minkowski algebra. The other is based on the construction of 5-dimensional matrix representation of the κ-Minkowski coordinate algebra. Neither approach leads to a unique construction. Here, we find the relation between these two approaches and introduce a unified approach, capable of describing all momentum spaces, and identify the corresponding quantum group of spacetime symmetries. We reproduce known results and get a few new ones. In particular, we describe the three momentum spaces associated to the κ-Poincaré group, which are half of a de Sitter, anti-de Sitter or Minkowski space, and we identify what distinguishes them. Moreover, we find a new momentum space with the geometry of a light cone, associated to a κ-deformation of the Carroll group.
We present a framework which unifies a large class of noncommutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime ...coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Lorentz transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.
We study the Lie bialgebra structures that can be built on the one-dimensional central extension of the Poincaré and (A)dS algebras in (1 + 1) dimensions. These central extensions admit more than one ...interpretation, but the simplest one is that they describe the symmetries of (the noncommutative deformation of) an Abelian gauge theory,
U
(1) or
SO
(2) on Minkowski or (A)dS spacetime. We show that this highlights the possibility that the algebra of functions on the gauge bundle becomes noncommutative. This is a new way in which the Coleman–Mandula theorem could be circumvented by noncommutative structures, and it is related to a mixing of spacetime and gauge symmetry generators when they act on tensor-product states. We obtain all Lie bialgebra structures on centrally-extended Poincaré and (A)dS which are coisotropic w.r.t. the Lorentz algebra, and therefore admit the construction of a noncommutative principal gauge bundle on a quantum homogeneous spacetime. It is shown that several different types of hybrid noncommutativity between the spacetime and gauge coordinates are allowed. In one of these cases, an alternative interpretation of the central extension leads to a new description of the well-known canonical noncommutative spacetime as the quantum homogeneous space of a quantum Poincaré algebra.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ...ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics – it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.
Recent work showed that κ-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the ...Poincaré algebra of special-relativistic symmetries, one can toggle the curvature parameter Λ, the Planck scale quantum deformation parameter κ and the speed of light parameter c to move to the well-studied κ-Poincaré algebra, the (quantum) (A)dS algebra, the (quantum) Galilei and Carroll algebras and their curved versions. In this review, we survey the properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.
We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary ...configuration space with respect to the similarity group of total translations, rotations, and scalings. For the zero-energy gravitating N-body system, the dynamics on shape space can be constructed explicitly and the points of total collision, which are the points of central configuration and zero shape momenta, can be analyzed in detail. It turns out that, even on shape space where scale is not part of the description, the equations of motion diverge at (and only at) the points of total collision. We construct and study the stratified total-collision manifold and show that, at the points of total collision on shape space, the singularity is essential. There is, thus, no way to evolve solutions through these points. This mirrors closely the big bang singularity of general relativity, where the homogeneous-but-not-isotropic cosmological model of Bianchi IX shows an essential singularity at the big bang. A simple modification of the general-relativistic model (the addition of a stiff matter field) changes the system into one whose shape-dynamical description allows for a deterministic evolution through the singularity. We suspect that, similarly, some modification of the dynamics would be required in order to regularize the total collision singularity of the N-body model.
Singularities in General Relativity are regions where the description of spacetime in terms of a pseudo-Riemannian geometry breaks down. The theory seems unable to predict the evolution of the ...physical degrees of freedom around and beyond such regions. In a recent paper, the author and collaborators challenged this view by providing an example of a singularity at which Einstein's equations can be rewritten in a form that satisfies an existence and uniqueness theorem, thereby predicting that each solution can be continued uniquely through the singularity. This result was obtained under the assumption of homogeneity (but not isotropy), and requires the presence of a massless free scalar field. This paper extends the result to N scalar fields with a potential, the only requirement being that it does not grow too fast. In particular, the result is compatible with inflationary potentials, e.g. Starobinsky's. This brings us one step closer to the goal of extending the original result to realistic cosmologies.
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