Related papers: Lorentz covariant spin two superspaces
We present a theoretical framework called Lorentz quantum mechanics, where the dynamics of a system is a complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary…
The distinct models that describe spin 1 and 2 massive excitations in 2+1 dimensions are analized, showing their equivalence (between models of same spin) and analogies (between models of different spin). Topics as spontaneous symmetry…
We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional…
In the framework of light-cone gauge formulation, massless arbitrary spin N=1 supermultiplets in four-dimensional flat space are considered. We study both the integer (super)spin and half-integer (super)spin supermultiplets. For such…
We present a derivation of a position operator for a massive field with spin $1/2$, expressed in a representation-independent form of the Poincar\'e group. Using the recently derived Lorentz-covariant field spin operator, we obtain a…
A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the Dunkl oscillator model in the plane, whose Hamiltonian…
It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a…
Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…
We investigate a Lorentz invariant action which is quadratic in two rank-2 symmetric tensor fields in Minkowski spacetime. We apply a scalar-vector-tensor decomposition to two tensor fields by virtue of 3-dimensional rotation-invariance of…
Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…
We display the construction of a twisted superalgebra for the N=1 Euclidian supergravity on 4-manifolds with an almost complex structure. It acts on a representation of twisted supersymmetry made of forms with odd and even statistics and it…
The Helmholtz equation for symmetric, traceless, second-rank tensor fields in three-dimensional flat space is solved in spherical and cylindrical coordinates by separation of variables making use of the corresponding spin-weighted…
We present a Lagrangian theory of gravitation that develops some ideas proposed several years ago. It is formulated on the 10-dimensional space $\mathcal{S}$ of the local Lorentz frames (tetrads) and it is covariant under the symplectic…
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two…
In $\mathcal{N}=1$ superconformal theories in four dimensions the two-point function of superconformal multiplets is known up to an overall constant. A superconformal multiplet contains several conformal primary operators, whose two-point…
Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and…
We discuss symmetry fractionalization of the Lorentz group in (2+1)$d$ non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are…
We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use…
We describe and solve three puzzles arising in covariant and supertranslation-invariant formulas for the flux of angular momentum and other Lorentz charges in asymptotically flat spacetimes: 1) Supertranslation-invariance and covariance…
Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor $\lambda_{a}$ and Ramond grassmannian vector $\psi_{m}=-{1\over 2}(\bar\theta\gamma_{m}\lambda)$ in the spinor…