439 research outputs found
Fourier analysis on the affine group, quantization and noncompact Connes geometries
We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of
the line. A noncommutative product of functions on the half-plane, underlying a
noncompact spectral triple in the sense of Connes, is obtained from it. The
corresponding Wigner functions reproduce the time-frequency distributions of
signal processing. The same construction leads to scalar Fourier
transformations on the affine group, simplifying and extending the Fourier
transformation proposed by Kirillov.Comment: 37 pages, Latex, uses TikZ package to draw 3 figures. Two new
subsections, main results unchange
Diphoton decay of the higgs from the Epstein--Glaser viewpoint
We revisit a nearly ten-year old controversy on the diphoton decay of the
Higgs particle. To a large extent, the controversy turned around the respective
merits of the regularization techniques employed. The novel aspect of our
approach is that no regularization techniques are brought to bear: we work
within the Bogoliubov--Epstein--Glaser scheme of renormalization by extension
of distributions. Solving the problem actually required an expansion of this
method's toolkit, furnished in the paper.Comment: 45 pages, to appear in Eur. Phys. J.
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