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Velhinho, "Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes," Physical Review D: Particles, Fields, Gravitation and Cosmology, vol.
Velhinho, "Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization," Annals of Physics, vol.
Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes
Looking at fields that evolve in the exterior region of a Kerry-Newman-de Sitter black hole, Daude and Nicoleau begin by establishing the existence and asymptotic completeness of time-dependent wave operators associated the Dirac fields they study.
One important distinction of the electromagnetic fields versus the Dirac fields is that the equations are second order.
The extension to the many particle case leads to a proliferation of functions akin to the rapid number of increasing spin states for multiple Dirac fields. In each time direction of a two photon state [A.sup.[mu]v]([x.sup.[alpha]], [y.sup.[beta]]) we need first and second order time derivatives.
They include thorough analyses of the data and the emergent theories as they cover quantized Dirac fields
, the standard model, three-generation mixing, neutrino interactions, massive neutrinos, neutrino oscillations in vacuum and the associated theory, neutrino oscillations in matter, solar neutrinos, atmospheric neutrinos, terrestrial neutrino oscillation experiments, phenomenology of three-neutrino mixing, direct measurements of neutrino mass, supernova neutrinos, cosmology, and relic neutrinos.
For example, the Dirac fields do not commute at spacelike separation.
We treat the field classically to start with, so one can think of [Psi] as a (first-quantized) Schrodinger field, or if we want to be relativistic a Klein-Gordon or Dirac field. The Lagrangian for the matter field is invariant under global phase transformations [Psi](x) [approaches] [Psi](x) [e.sup.i[Theta]], which leads via Noether's theorem to the conservation of charge.
In this context, we consider the nonminimal coupling of the Dirac field
to torsion in the context of teleparallel theory of gravity in 2+1 dimensional Weitzenbockspace-time to investigate whether Dirac fields
may be responsible for the early-time inflation and late-time acceleration.
Initially we need to reconsider some aspects of the particular fields in our study: the metric, electromagnetic and Dirac fields
. The Dirac equation is interesting as a spinor construction with no explicit metric but an algebra of gamma-matrices that induce the Minkowskii geometry and causal structure.