Relativistic Wave Equations for Particles with Arbitrary Spin

Abstract

Relativistic wave equations a r e derived which generalize the recently obtained Galileic o~a r i a n t wave equations for massive particles with any integer or half-integer spin. Imposing a minimality condition on the number of components possessed by the relativistic wave function, it i s shown that the index transformation properties of the wave function may be either those of the (s, 0)% (S -8 , 4 ) representation of SL(2, C) o r of the representation (0, s),b($, s -6 ) . The minimal extension of these representations which accommodates reflection symmetry yields the Dirac equation for s = $, the Duffin-Kemmer equation for s = 1, and an equation for particles with s > 1 whose wave-function indices transform according to the (s, 0 ) 7 ( s -4, $ ),i3(;, s -a )-4(0, s ) representation of SL(2,C). The latter theory possesses 4(2s + 1) independent components, has no subsidiary conditions, and describes a unique mass, m*O, and a unique spin. The theory admits a simple Lagrangian and Hamiltonian formulation and yields a conserved current. Finally, it i s shown that for any spin the equation remains consistent and causal in the presence of a minimally coupled external-electromagnetic-field interaction.

Pair Production and Vacuum Polarization of Arbitrary Spin Particles with EDM and AMM

“…Equation (1) at the case σ = 0 was investigated in [18], and at the particular case of the "normal" magnetic moment of a particle, when g = 1/s, we arrive at the approach [10]. Here arbitrary AMM and EDM of a particle is considered.…”

“…In the case of a "normal" magnetic moment and the absence of the EDM, such a scheme was introduced in [10]. The wave function in this approach has the minimal number 2(2s + 1) of components, and particles propagate causally in external electromagnetic fields.…”

A first-order Lagrangian theory of fields with arbitrary spin

“…In comparison to the neatness of the Dirac theory of one-half-spin fields, formulations of arbitrary-spin field theories suffer various complications [1,32,2,21,22]. Usual approaches proceed by considering fields with many spinor and/or spacetime indices, possibly constrained by symmetry conditions.…”

Some solved problems of the periodic system of chemical elements

“…3 3 The rather involved theory of multivalued representations of the rotational group, generalized to n dimensions, might be applied to create the spin in n dimensions, compare Ref. 34. …”