
SIGMA 1 (2005), 028, 8 pages quantph/0512228
http://dx.doi.org/10.3842/SIGMA.2005.028
Representations of U(2∞) and the Value of the Fine Structure Constant
William H. Klink
Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa, USA
Received September 28, 2005, in final form December 17, 2005; Published online December 25, 2005
Abstract
A relativistic quantum mechanics is formulated in which
all of the interactions are in the fourmomentum operator and
Lorentz transformations are kinematic. Interactions are
introduced through vertices, which are bilinear in fermion and
antifermion creation and annihilation operators, and linear in
boson creation and annihilation operators. The fermionantifermion
operators generate a unitary Lie algebra, whose representations
are fixed by a first order Casimir operator (corresponding to
baryon number or charge).
Eigenvectors and eigenvalues of the fourmomentum operator
are analyzed and exact solutions in the strong coupling limit
are sketched. A simple model shows how the fine
structure constant might be determined for the QED vertex.
Key words:
point form relativistic quantum mechanics; antisymmetric
representations of infinite unitary groups; semidirect sum of
unitary with Heisenberg algebra.
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