Related papers: New class of spin projection operators for 3D mode…
We propose a new basis of spin-operators, specific for the case of planar theories, which allows a Lagrangian decomposition into spin-parity components. The procedure enables us to discuss unitarity and spectral properties of gravity models…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We elaborate on the spin projection operators in three dimensions and use them to derive a new representation for the linearised higher-spin Cotton tensors.
These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an…
In this PhD thesis, we investigate a wide class of three-dimensional massive gravity models and show how most of them (if not all) can be brought in a first-order, Chern-Simons-like, formulation. This allows for a general analysis of the…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…
Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The classical and quantum properties of the higher-spin theory depend crucially on the embedding…
We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher…
Scientific imaging techniques such as optical and electron microscopy and computed tomography (CT) scanning are used to study the 3D structure of an object through 2D observations. These observations are related to the original 3D object…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
We study holography of the 3d Chern-Simons theory as a gauge theory of $so(3,2)$, $sl_4$ and $sl_5$ algebras. For the near horizon boundary conditions we comment solutions from several projectors from Chern-Simons to the metric formulation.…
Extending the works arXiv:1504.05991 and arXiv:1510.02142, we study three dimensional Euclidean higher spin gravity with negative cosmological constant. This theory can be formulated in terms of SL(N,C) Chern-Simons theory. By introducing…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
These notes aim at providing a pedagogical and pedestrian introduction to the subject and assume no previous knowledge apart from that of general relativity. We shall first recall the "frame" formulation of the later theory, then…
We present a new representation of spin operators in terms of bosonic creation-annihilation operators. This representation allows us to formulate a new field-theoretical description of spin systems which is free of any constraints. The…
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge…
We introduce and investigate new models of the Chern-Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used…
We have limited our interaction scope to those involving particle-s spin. We then develop operators for handling a many-body treatment of the spin interactions. The results presented show how to promote the particles of the system into the…
The particle content of the Singh-Hagen model ($SH$) in $D$ dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and…