SIGMA, 2005, Volume 1, 028, 8 pages
Representations of $U(2\infty)$ and the Value of the Fine Structure Constant
William H. Klink
Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa, USA
A relativistic quantum mechanics is formulated in which all of the interactions are in the four-momentum 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 fermion-antifermion 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 four-momentum 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.
point form relativistic quantum mechanics; antisymmetric representations of infinite unitary groups; semidirect sum ofunitary with Heisenberg algebra
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MSC: 22D10; 81R10; 81T27
Received: September 28, 2005; in final form December 17, 2005; Published online December 25, 2005
William H. Klink, “Representations of $U(2\infty)$ and the Value of the Fine Structure Constant”, SIGMA, 1 (2005), 028, 8 pp.
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\by William H. Klink
\paper Representations of $U(2\infty)$ and the Value of the Fine Structure Constant
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