21 research outputs found
Negative Energies in the Dirac equation
It is easy to check that both algebraic equation Det (hat p - m) =0 and Det
(hat p + m) =0 for u- and v- 4-spinors have solutions with p_0= pm E_p = pm
sqrt bf p^2 +m^2. The same is true for higher-spin equations. Meanwhile, every
book considers the equality p_0=E_p for both u- and v- spinors of the
(1/2,0)+(0,1/2)) representation only, thus applying the
Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy
solutions. The recent Ziino works (and, independently, the articles of several
others) show that the Fock space can be doubled. We re-consider this
possibility on the quantum field level for both s=1/2 and higher spin
particles.Comment: 8 pages, no figures. Accepted in Zeitschrift fur Naturforschun
The 2(2S+1)- Formalism and Its Connection with Other Descriptions
In the framework of the Joos-Weinberg 2(2S+1)- theory for massless particles,
the dynamical invariants have been derived from the Lagrangian density which is
considered to be a 4- vector. A la Majorana interpretation of the 6- component
"spinors", the field operators of S=1 particles, as the left- and
right-circularly polarized radiation, leads us to the conserved quantities
which are analogous to those obtained by Lipkin and Sudbery. The scalar
Lagrangian of the Joos-Weinberg theory is shown to be equivalent to the
Lagrangian of a free massless field, introduced by Hayashi. As a consequence of
a new "gauge" invariance this skew-symmetric field describes physical particles
with the longitudinal components only. The interaction of the spinor field with
the Weinberg's 2(2S+1)- component massless field is considered. New
interpretation of the Weinberg field function is proposed. KEYWORDS: quantum
electrodynamics, Lorentz group representation, high-spin particles, bivector,
electromagnetic field potential. PACS: 03.50.De, 11.10.Ef, 11.10.Qr, 11.17+y,
11.30.CpComment: 13pp., merged hep-th/9305141 and hep-th/9306108 with revisions.
Accepted in "Int. J. Geom. Meth. Phys.