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A structural explanation of the coupling constants in the standard model, i.ethe fine structure constant and the Weinberg angle, and of the gauge fixingcontributions is given in terms of symmetries and representation theory. Thecoupling constants are normalizations of Lorentz invariantly embedded littlegroups (spin and polarization) arising in a harmonic analysis of quantum vectorfields. It is shown that the harmonic analysis of massless fields requires anextension of the familiar Fourier decomposition, containing also indefiniteunitary nondecomposable time representations. This is illustrated by thenonprobabilistic contributions in the electromagnetic field.Comment: 18 pages LaTeX file (62 kB), all macros are include

Quantum fieldà la Sylvester and Witt