Symmetry, Integrability and Geometry: Methods and Applications, 2017
We present an in-depth investigation of the SL(2, R) momentum space describing point particles co... more We present an in-depth investigation of the SL(2, R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2, R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them.
This paper is the first in a series of three. The second paper gives the details of the explicit ... more This paper is the first in a series of three. The second paper gives the details of the explicit construction of the Coulomb branch geometries discussed here, while the third discusses the computation of central charges of the associated SCFTs.
Symmetry, Integrability and Geometry: Methods and Applications, 2017
We present an in-depth investigation of the SL(2, R) momentum space describing point particles co... more We present an in-depth investigation of the SL(2, R) momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincaré group: the quantum double of SL(2, R). We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them.
This paper is the first in a series of three. The second paper gives the details of the explicit ... more This paper is the first in a series of three. The second paper gives the details of the explicit construction of the Coulomb branch geometries discussed here, while the third discusses the computation of central charges of the associated SCFTs.
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Papers by Matteo Lotito