Relativistic wave equations for interacting, massive particles with arbitrary half-integer spins

Abstract

New relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank 2n (n = s − 1 2 ) antisymmetric w.r.t. n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.

Bosonic and fermionic Weinberg-Joos (j,0) ⊕ (0,j) states of arbitrary spins as Lorentz tensors or tensor-spinors and second-order theory

“…Moreover, differently from the present work, no physical observables have been calculated in [22] for the sake of a comparison to predictions by other formalisms. Finally, the scheme of [22] confines to fractional spins alone, while the one elaborated here applies to both fermions and bosons. , 0 ⊕ 0, 3 2 as part of the anti-symmetric Lorentz tensor-spinor of second rank…”

“…However, the focus of [22] has been in first place the separation of parities, while the question on the precise assignment of spin- 3 2 to the irreducible 3 2 , 0 ⊕ 0, 3 2 sector of the anti-symmetric tensor spinor of second rank has been left aside. Moreover, differently from the present work, no physical observables have been calculated in [22] for the sake of a comparison to predictions by other formalisms. Finally, the scheme of [22] confines to fractional spins alone, while the one elaborated here applies to both fermions and bosons.…”

“…Fermionic representation spaces of the types (2), (4) have been earlier employed by Niederle and Nikitin in [22] in a linear framework of the RaritaSchwinger type, with the special emphasis on spin- 3 2 . However, the focus of [22] has been in first place the separation of parities, while the question on the precise assignment of spin- 3 2 to the irreducible 3 2 , 0 ⊕ 0, 3 2 sector of the anti-symmetric tensor spinor of second rank has been left aside.…”

Local current operators for arbitrary spin particles

“…But unlike wave equations, where additional constraints are imposed on the wave function solutions of the wave equations, extracting the static properties from matrix elements of current operators does not involve any constraints. As is well known these additional constraints imposed on wave functions lead to acausal properties for higher spin particles [4]. Further work is required to see what happens when the currents for higher spin particles given in this paper are coupled to an external electromagnetic field via the interaction given in Eq.11.…”

“…In both cases the electromagnetic interaction is formed by coupling the current operators described in this paper to the photon field, analyzed in detail in the next paper in this series [3], to form the electromagnetic vertex for arbitrary spin particles with arbitrary form factors. And if these currents are coupled to a classical field, it becomes possible to investigate some of the so-called acausal behavior of high spin particles in an external electromagnetic field [4]. More generally this series of papers begins an investigation of many-body relativistic theories in the point form, in which the interacting four-momentum operator is given solely in terms of creation and annihilation operators with arbitrary form factors.…”