arXiv subjects

Mattia Manfredonia

Publications and source records attributed to Mattia Manfredonia.

6 recordsLinked to original sources

arXiv2021

The Weyl-Mellin quantization map for $κ$-Minkowski Noncommutative Spacetime

We present a quantization of the functions of spacetime, i.e.\ a map, analog to Weyl map, which reproduces the $κ$-Minkowski commutation relations, and it has the desirable properties of mapping square integrable funcions into Hilbert-Schmidt operators, as well as real functions into self-adjoint operators. The map is based on Mellin transform on radial and time coordinates. The map also define a deformed $*$ product which we discuss with examples.

hep-th↗

arXiv2020

The Momentum Spaces of $κ$-Minkowski noncommutative spacetime

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.

hep-th↗

arXiv2019

Localizability in $κ$-Minkowski Spacetime

Using the methods of ordinary quantum mechanics we study $κ$-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging arXiv:1811.08409. We see how the role of Fourier transforms is played in this case by Mellin transforms. We briefly discuss the role of transformations and observers.

hep-th↗

arXiv2018

Localization and Reference Frames in $κ$-Minkowski Spacetime

We study the limits to the localizability of events and reference frames in the $κ$-Minkowski quantum spacetime. Our main tool will be a representation of the $κ$-Minkowski commutation relations between coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizability properties of states both in space and time. We then discuss the transformation rules between inertial observers, which are described by the quantum $κ$-Poincaré group. These too are subject to limitations in the localizability of states, which impose further restrictions on the ability of an observer to localize events defined in a different observer's reference frame.

hep-th↗

arXiv2018

Spin, torsion and violation of null energy condition in traversable wormholes

The static spherically symmetric traversable wormholes are analysed in the Einstein- Cartan theory of gravitation. In particular, we computed the torsion tensor for matter fields with different spin S = 0; 1/2; 1; 3/2. Interestingly, only for certain values of the spin the torsion contribution to Einstein-Cartan field equation allows one to satisfy both faring-out condition and Null Energy Condition. In this scenario traversable wormholes can be produced by using usual (non-exotic) spinning matter.

gr-qc↗

arXiv2017

Characterising exotic matter driving wormhole

In this paper, we develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method, based on a Taylor expansion of metric and stress-energy tensor components in a neighbourhood of the wormhole throat, reduces the Einstein equations to an infinite set of algebraic conditions, which can be satisfied order by order. The approach easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state. The method is then applied to some relevant examples of exotic matter characterised by a constant energy density and that also show an isotropic behaviour in the stress-energy tensor or obeying to a quintessence-like equation of state.

gr-qc↗