Quantum Fields a la Sylvester and Witt

A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling constants are normalizations of Lorentz invariantly embedded little groups (spin and polarization) arising in a harmonic analysis of quantum vector fields. It is shown that the harmonic analysis of massless fields requires an extension of the familiar Fourier decomposition, containing also indefinite unitary nondecomposable time representations. This is illustrated by the nonprobabilistic contributions in the electromagnetic field.Comment: 18 pages LaTeX file (62 kB), all macros are include

Relativities and Homogeneous Spaces I -- Finite dimensional relativity representations

Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and isospin group, on the other side, are discussed under the common concept of "relativity". A relativity is defined by classes $G/H$ of a "little" group in a "general" group of operations.Relativities are representable as linear transformations that are considered for five physically relevant examples.Comment: 23 page

Matter as Spectrum of Spacetime Representations

Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators. The representation invariants arise as singularities of rational representation functions in the complex energy and complex momentum plane. The homogeneous space $GL(2,C)/U(2)$ with rank 2, the orientation manifold of the unitary hypercharge-isospin group, is taken as model of nonlinear spacetime. Its representations are characterized by two continuous invariants whose ratio will be related to gauge field coupling constants as residues of the related representation functions. Invariants of product representations define unitary Poincar\'e group representations with masses for free particles in tangent Minkowski spacetime.Comment: 37 pages, latex, macros include