Related papers: Lorentz covariant spin two superspaces
We present a framework which unifies a large class of non-commutative 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…
J. G. Thompson showed that a finite group G is solvable if and only if every two -generated subgroup is solvable. Recently, Grunevald, Kunyavskii, Nikolova, and Plotkin have shown that the analogue holds for finite-dimensional Lie algebras…
This paper explores the existence of kinematical gauge transformations for Lorentz invariant equations which describe a multiplet of two spin $\frac{1}{2}$ particles. For this multiplet the additional gauge invariance can be in form of…
We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, $f(T,\phi)$, thus encompassing the cases of $f(T)$ gravity and nonminimally coupled…
In a space of $d=15 $ Grassmann coordinates, two types of generators of the Lorentz transformations, one of spinorial and the other of vectorial character, both linear operators in Grassmann space, forming the group $ SO(1,14) $ which…
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each…
The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with…
Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in…
In this article we present a new C*-algebraic deformation of the Lorentz group. It is obtained by means of the Rieffel deformation applied to SL(2,C). We give a detailed description of the resulting quantum group in terms of generators -…
The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic…
Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this…
The basic mathematical framework for super Hilbert spaces over a Grassmann algebra with a Grassmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Grassmann algebras arise in the functional…
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…
Two-dimensional quantum fields in electric and gravitational backgrounds can be described by conformal field theories, and hence all the physical (covariant) quantities can be written in terms of the corresponding holomorphic quantities. In…
We show that the torsion of a Cartan geometry can be associated to two spin-2 fields. This structure allows a new approach to deal with the proposal of geometrization of spin-2 fields besides the traditional one dealt with in General…
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…
We derive a relativistic-covariant spin operator for massive case directly from space-time symmetry in Minkowski space-time and investigate the physical properties of a derived spin operator. In the derivation we require only two…
We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at…