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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 spin 1/2 and 1 (Dirac and Maxwell fields) are considered in detail on the eight-dimensional homogeneous space, which is equivalent to a direct product of Minkowski spacetime and two-dimensional complex sphere. It is shown that a massless spin-1 field, corresponding to a photon field, should be defined within principal series representations of the Lorentz group. Interaction between spin-1/2 and spin-1 fields is studied in terms of a trilinear form. An analogue of the Dyson formula for $S$-matrix is introduced on the eight-dimensional homogeneous space. It is shown that in this case elements of the $S$-matrix are defined by convergent integrals.
We show how to get a non-commutative product for functions on space-time starting from the deformation of the coproduct of the Poincare group using the Drinfeld twist. Thus it is easy to see that the commutative algebra of functions on space-time (R^
We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical $r$-matrices associated with $kappa$-deformations of the Poincare algebra. These classical $kappa$-Poincare $r$-matrices describe three kinds of deformatio
Relativistic spin states are convention dependent. In this work we prove that the zero momentum-transfer limits of the leading two form factors in the decomposition of the energy-momentum tensor matrix elements are independent of this choice. In part
In this work we analyse the constraints imposed by Poincare symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distribu
A spinless covariant field $phi$ on Minkowski spacetime $M^{d+1}$ obeys the relation $U(a,Lambda)phi(x)U(a,Lambda)^{-1}=phi(Lambda x+a)$ where $(a,Lambda)$ is an element of the Poincare group $Pg$ and $U:(a,Lambda)to U(a,Lambda)$ is its unitary repre