It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the threeparameter rotation subgroup and the three-parameter Lorentz group for two spatial and one time dimensions. It is noted that the Lorentz group has another three-parameter ...

The subject of this work is analysis of hadronic decays of exotic meson π1 in a fully relativistic formalism, and comparison with the nonrelativistic results. The relativistic spin wave functions of mesons and hybrids are constructed based on unitary representations of the Lorentz group. The radial wave functions are obtained from phenomenological considerations of the mass operator. We find th...

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L functions on three-dimensional hyperbolic space. To ‘evaluate’ such a ...

Resummation of target mass corrections in two-photon processes: twist-two sector. Abstract We develop a formalism for the resummation of target mass corrections in off-forward two-photon amplitudes given by a chronological product of electromagnetic currents, arising in e.g. deeply virtual Compton scattering. The method is based on a relation of composite operators with a definite twist to harm...

In these notes, I discuss the relation of relativistic invariance to quantum mechanics. First, I discuss the rotation group and its representations. Then I outline the structure of Lorentz group and build up the finite dimensional representations of the Lorentz Group. Finally, I add the space and time translations to get the Poincaré group. This allows us to find how to treat the spin of partic...

We continue from Part 1. We will illustrate the general theory of Hamiltonian mechanics in the Lie group formalism. We then obtain the Hamiltonian formalism in the Hilbert spaces of square integrable functions on the symplectic spaces. We illustrate this general theory with several concrete examples, two of which are the representations of the Lorentz group and the Poincaré group with interacti...

We give a framework to describe gauge theory on a certain class of commutative but nonassociative fuzzy spaces. Our description is in terms of an Abelian gauge connection valued in the algebra of functions on the cotangent bundle of the fuzzy space. The structure of such a gauge theory has many formal similarities with that of Yang-Mills theory. The components of the gauge connection are functi...

We show that the triple product defined by the spin domain (Bounded Symmetric Domain of type 4 in Cartan’s classification) is closely related to the geometric product in Clifford algebras. We present the properties of this tri-product and compare it with the geometric product. The spin domain can be used to construct a model in which spin 1 and spin1/2 particles coexist. Using the geometric tri...