Related papers: Relativistic Particle on Light-Front
There is ambitious pretension formulated by Weinberg \cite{W} that {\it any relativistic quantum theory will look at sufficiently low energy like a quantum field theory.} It is based on the observation that for formulation of quantum field…
Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase…
On-shell, analytic S-matrix elements in massless theories are constructed from a finite set of primitive three-point amplitudes, which are fixed by Poincare invariance up to an overall numerical constant. We classify \emph{all} such…
Starting with the generators of the Poincar\'e group for arbitrary mass (m) and spin (s) a nonunitary transformation is implemented to obtain momenta with an absolute Planck scale limit. In the rest frame (for $m>0$) the transformed energy…
First the "frame problem" is sketched: the motion of an isolated particle obeys a simple law in galilean frames, but how does the galilean character of the frame manifest itself at the place of the particle? A description of vacuum as a…
To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the…
We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
The two-by-two representation of the SL(2,c) group is for spin-1/2 particles. Starting from this two-by-two representation, it is possible to construct the four-by-four matrices for spin-1 particles. For massless particles, it is possible…
We identify an extended Poincare symmetry $ISO(2) \times ISO(3,1)$ for on-shell massive scattering amplitudes, transforming under the $U(2)$ Little group symmetry. Thus the one-particle state involves in both spin and transversality $t$…
The Inonu-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of…
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…
An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic…
In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical…
A detailed study of certain apspects of some 2+1 dimensional field theories is presented with special emphasis on the role of Wigner's little group for massless particles in generating gauge transformations. The planar models considered…
Particles states transforming in one of the infinite spin representations of the Poincar\'e group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state…