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Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice
We propose the fundamental and two dimensional representation of the Lorentz
groups on a (3+1)-dimensional hypercubic lattice, from which representations of
higher dimensions can be constructed. For the unitary representation of the
discrete translation group we use the kernel of the Fourier transform. From the
Dirac representation of the Lorentz group (including reflections) we derive in
a natural way the wave equation on the lattice for spin 1/2 particles. Finally
the induced representation of the discrete inhomogeneous Lorentz group is
constructed by standard methods and its connection with the continuous case is
discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission
Detector developments for the hypernuclear programme at PANDA
The technical design of the PANDA experiment at the future FAIR facility next
to GSI is progressing. At the proposed anti-proton storage ring the
spectroscopy of double Lambda hypernuclei is one of the four main topics which
will be addressed by the Collaboration. The hypernuclear experiments require
(i) a dedicated internal target, (ii) an active secondary target of alternating
silicon and absorber material layers, (iii) high purity germanium (HPGe)
detectors, and (iv) a good particle identification system for low momentum
kaons. All systems need to operate in the presence of a high magnetic field and
a large hadronic background. The status of the detector developments for this
programme is summarized.Comment: Contributed to 2008 IEEE Nuclear Science Symposium, 19-25 October
2008, Dresden, German
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