2,319 research outputs found
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 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 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
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