12,097 research outputs found
Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory
We propose a general method for the description of arbitrary single spin-j
states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz
algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for
fermions, and by means of second order Lagrangians. The method allows to avoid
the cumbersome matrix calculus and higher \partial^{2j} order wave equations
inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor
(tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible
sector and design there a representation reduction algorithm based on one of
the Casimir invariants of the Lorentz algebra. This algorithm allows us to
separate neatly the pure spin-j sector of interest from the rest, while
preserving the separate Lorentz- and Dirac indexes. However, the Lorentz
invariants are momentum independent and do not provide wave equations. Genuine
wave equations are obtained by conditioning the Lorentz-tensors under
consideration to satisfy the Klein-Gordon equation. In so doing, one always
ends up with wave equations and associated Lagrangians that are second order in
the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2)
is comfortably described by a second order Lagrangian in the basis of the
totally antisymmetric Lorentz tensor-spinor of second rank, \Psi_[ \mu\nu].
Moreover, the particle is shown to propagate causally within an electromagnetic
background. In our study of (3/2,0)+(0,3/2) as part of \Psi_[\mu\nu] we
reproduce the electromagnetic multipole moments known from the Weinberg-Joos
theory. We also find a Compton differential cross section that satisfies
unitarity in forward direction. The suggested tensor calculus presents itself
very computer friendly with respect to the symbolic software FeynCalc.Comment: LaTex 34 pages, 1 table, 8 figures. arXiv admin note: text overlap
with arXiv:1312.581
Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces
Structure of eigenstates in a periodic quasi-1D waveguide with a rough
surface is studied both analytically and numerically. We have found a large
number of "regular" eigenstates for any high energy. They result in a very slow
convergence to the classical limit in which the eigenstates are expected to be
completely ergodic. As a consequence, localization properties of eigenstates
originated from unperturbed transverse channels with low indexes, are strongly
localized (delocalized) in the momentum (coordinate) representation. These
eigenstates were found to have a quite unexpeted form that manifests a kind of
"repulsion" from the rough surface. Our results indicate that standard
statistical approaches for ballistic localization in such waveguides seem to be
unappropriate.Comment: 5 pages, 4 figure
Coupling of Nitrogen-Vacancy Centers to Photonic Crystal Cavities in Monocrystalline Diamond
The zero-phonon transition rate of a nitrogen-vacancy center is enhanced by a
factor of ~70 by coupling to a photonic crystal resonator fabricated in
monocrystalline diamond using standard semiconductor fabrication techniques.
Photon correlation measurements on the spectrally filtered zero-phonon line
show antibunching, a signature that the collected photoluminescence is emitted
primarily by a single nitrogen-vacancy center. The linewidth of the coupled
nitrogen-vacancy center and the spectral diffusion are characterized using
high-resolution photoluminescence and photoluminescence excitation
spectroscopy
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