Related papers: Currents for Arbitrary Helicity
In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincar\'e group. We define a weaker…
Reviewing the construction of induced representations of the Poincar\'e group of four-dimensional spacetime we find all massive representations, including the ones acting on interacting many-particle states. Massless momentum wavefunctions…
Studies of scattering amplitudes for electric and magnetic charges have identified previously overlooked multiparticle representations of the Poincar\'e group in four dimensions. Such representations associate nontrivial quantum numbers…
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…
The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting the conservation law only holds under the assumption that the…
In this work we extend the definition of asymptotic multi-particle states of the $S$-matrix, beyond the direct products of one-particle states. We identify new quantum numbers which we call pairwise helicities, or $q_{ij}$, associated with…
We discuss new bounds on vectors coupled to currents whose non-conservation is due to mass terms, such as $U(1)_{L_\mu - L_\tau}$. Due to the emission of many final state longitudinally polarized gauge bosons, inclusive rates grow…
We build coherent states (CS) for unbounded motions along two different procedures. In the first one we adapt the Malkin-Manko construction for quadratic Hamiltonians to the motion of a particle in a linear potential. A generalization to…
The existence of a second quadratic inviscid invariant, the helicity, in a turbulent flow leads to coexisting cascades of energy and helicity. An equivalent of the four-fifth law for the longitudinal third order structure function, which is…
This paper gives a $p$-adic analogue of the Mackey theory, which relates representations of a group of type $G=H\times_{t} A $ to systems of imprimitivity.
We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…
At intermediate energies it appears advantageous to work without partial wave decomposition and use directly the momentum vectors. We derived a finite set of coupled Lippmann-Schwinger equations using helicities. They can be used for any…
We study density currents associated with a collection of positive closed (1,1)-currents. We prove that the density current is unique and determined by the usual wedge product in some classical situations including the case where the…
We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.
We present a new approach to the definition of optical helicity in a medium. Our approach resolves the problem that duality transformations which simultaneously combine $\mathbf{E}$ with $\mathbf{H}$ and $\mathbf{D}$ with $\mathbf{B}$ are…
The aim of this paper is to compare singularities of closed positive currents whose non-pluripolar complex Monge--Amp\`ere masses equal. We also provide a short alternative proof for the monotonicity of non-pluripolar complex…
Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is…
In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincare' group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified…
Using group theoretical methods, we enumerate possible chiral representations in which hadron interpolating currents can be classified. We give simple examples of currents in each representation, some of which are well known. The…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…