Representations of U(2∞) and the Value of the Fine Structure Constant

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2005
• Main Author: Klink, W.H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209332
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Representations of U(2∞) and the Value of the Fine Structure Constant / W.H. Klink // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 7 назв. — англ.

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.