Related papers: A Derivation of Vector and Momentum Matrices
We study multipole decompositions of the electromagnetic currents of spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to reproduce representation specific wave equations which are second order in the momenta and…
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
We extend a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete spacetime. In so doing we…
We obtain the affine Euler-Poincar\'e equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin…
The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum…
We provide transformation matrices for arbitrary Lorentz transformations of multidimensional Hermite functions in any dimension. These serve as a valuable tool for analyzing spacetime properties of MHS fields, and aid in the description of…
Herein we shall consider Lorentz boosts and Wigner rotations from a (complexified) quaternionic point of view. We shall demonstrate that for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased…
We introduce two generalizations of bracket vectors from binary trees to permutrees. These new vectors help describe algebraic and geometric properties of the rotation lattice of permutrees defined by Pilaud and Pons. The first…
The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with…
The Proca-Corben-Schwinger equations for a spin-1 particle with an anomalous magnetic moment are added by a term describing an electric dipole moment, then they are reduced to a Hamiltonian form, and finally they are brought to the…
We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O($n=1$)…
It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost…
It is shown that the Pauli-Lubanski spin vector defined in terms of curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2 particles in noninertial motion along a curved trajectory. The possibility of detecting this…
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by…
The semi-inclusive correlator for a ${\cal J}$=1/2 bound-system, composed by A spin-1/2 fermions, is linearly expressed in terms of the light-front Poincar\'e covariant spin-dependent spectral function, in valence approximation. The…
We prove that, up to multiplication by a scalar, the Minkowski metric tensor is the only second-order tensor that is Lorentz-invariant. To prove this, we show that a specific set of three $4\times 4$ matrices, made of two rotation matrices…
Starting with an indecomposable Poincare module M_0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides…
We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry. The corresponding deformed…