Related papers: Zero mass as a Borel structure
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…
There are a number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 1/2. A great many equations with different C, P, T properties have been proposed and the impression could be formed that…
It is shown that electrons and photons can be considered as composities of particles representating the fundamental representation of the extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time which are held together by…
We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small,…
We show that the set of Liouville numbers is either null or non-$\sigma$-finite with respect to every translation invariant Borel measure on $\RR$, in particular, with respect to every Hausdorff measure $\iH^g$ with gauge function $g$. This…
The lightcone singularity at the origin is resolved by blowing up the singular point to $CP^1$. The Lorentz group acts on the resolved lightcone and has $CP^1$ as a special orbit. Using Wigner's method of associating unitary irreducible…
Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin 1/2. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz…
Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group $\tilde{G}_n=\widetilde{SO}_0(2,n)$ are investigated for $n\ge2$. It is found that, for space-time dimensions $n\ge3$, the situation…
We consider a microscopic analogue of the BMS analysis of asymptotic symmetries by analysing universal geometric structures on infinitesimal tangent light cones. Thereby, two natural microscopic symmetry groups arise: A non-trivially…
Massless black holes can be understood as bound states of a (positive mass) extreme a=\sqrt{3} black hole and a singular object with opposite (i.e. negative) mass with vanishing ADM (total) mass but non-vanishing gravitational field.…
It is noted that the Poincar\'e sphere for polarization optics contains the symmetries of the Lorentz group. The sphere is thus capable of describing the internal space-time symmetries dictated by Wigner's little groups. For massive…
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…
In an earlier paper we have constructed a basis of massless single particle quantum states which transform in the unitary principal series representation of the four dimensional Lorentz group. The S-matrix written in this basis gives rise…
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…
Linearized gravity is considered as an ordinary gauge field theory. This implies the need for gauge fixing in order to have well defined propagators. Only after having achieved this, the most general mass term is added. The aim of this…
We study the spatially homogeneous relativistic Boltzmann equation for massless particles in an FLRW background with scattering kernels in a certain range of soft and hard potentials. We obtain the future global existence of small solutions…
In the theory of the Dirac equation and in the standard model, the neutrino is massless. Both these theories use Lorentz invariance. In modern approaches however, spacetime is no longer smooth, and this modifies special relativity. We show…
Matter is coupled to three-dimensional gravity such that the topological phase is allowed and the (anti-) de Sitter or Poincar\'e symmetry remains intact. Spontaneous symmetry breaking to the Lorentz group occurs if a scalar field is…
Wigner's little group of a massless particle is ISO(2) which contains rotation and two translations. As well-known, eigenvalues of the rotation are helicity. On the other hand, by S. Weinberg et al., it has been shown that two translations…
Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation…