Interactions of aj=1 boson in the 2(2j+1) component theory

Abstract

The amplitudes for boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the used model is the Weinberg's 2(2j + 1) component formalism for describing a particle of spin j, recently developed substantially. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the ground of the hamiltonian formulation of quantum field theory on the mass hyperboloid, p 2 0 − p 2 = M 2 , proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T matrices for the fermion and the boson cases. However, certain differences are found. Possible physical applications are discussed.

The Feynman-Dyson propagators for neutral particles (locality or non-locality?)

“…It is necessary to consider all four equations, Eqs. (4)- (7). Obviously, this is related to the 12-component formalism, which I presented in [4].…”

“…But, it is interesting to note that the spin structure was proved there to be the same, regardless we consider the two-Dirac-fermion interaction or the two-Weinberg(S = 1)boson interaction. However, the denominator slightly differs (1/ ∆ 2 → 1/2m(∆ 0 − m)) in the cited papers [7] from the fermion-fermion case, where ∆ 0 , ∆ is the momentumtransger 4-vector in the Lobachevsky space. More accurate considerations of the fermion-boson and boson-boson interactions in the framework of the Weinberg theory has been reported elsewhere [8].…”

“…In Ref. [7] the amplitude for the interaction of two 2(2S + 1) bosons has been obtained on the basis of the use of one field only and it is obviously incomplete, see also Ref. [6].…”

The Feynman-Dyson propagators for neutral particles (locality or non-locality?)1

“…But, it is interesting to note that the spin structure was proved there to be the same, regardless we consider the two-Dirac-fermion interaction or the two-Weinberg(S = 1)-boson interaction. However, the denominator slightly differs (1/ ∆ 2 → 1/2m(∆ 0 − m)) in the cited papers [7] from the fermion-fermion case. More accurate considerations of the fermion-boson and boson-boson interactions in the framework of the Weinberg theory has been reported elsewhere [8].…”

Fermion-fermion and boson-boson amplitudes: surprising similarities

“…(Θ [1/2] , Θ [1] are the Wigner operators for spin 1/2 and 1, respectively). Recently, much attention has been paid to this formalism [12]. In refs.…”