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Representations of $U(2\infty)$ and the Value of the Fine Structure Constant
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: point form relativistic quantum mechanics; antisymmetric representations of infinite unitary groups; semidirect sum ofunitary with Heisenberg algebra. 
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William H. Klink. Representations of $U(2\infty)$ and the Value of the Fine Structure Constant. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a27/

[1] Klink W. H., “Point form relativistic quantum mechanics and electromagnetic form factors”, Phys. Rev. C, 58 (1998), 3587–3604 | DOI

[2] Keister B. D., Polyzou W. N., “Relativistic Hamiltonian dynamics in nuclear and particle physics”, Advances Nuclear Physics, 20, ed. J. W. Negele and E. W. Vogt, Plenum, New York, 1991, 225–479

[3] Barut A. O., Ra̧czka R., Theory of group representations and applications, Polish Scientific Publishers, Warsaw, 1977 | MR

[4] Tung W., Group theory in physics, World Scientific, Singapore, 1985 | MR

[5] Klink W. H., “Relativistic simultaneously coupled multiparticle states”, Phys. Rev. C, 58 (1998), 3617–3626 | DOI

[6] Zhelobenko D. P., Compact Lie groups and their representations, American Mathematical Society, Providence, R.I., 1973 | MR | Zbl

[7] Bargmann V., “On a Hilbert space of analytic functions and an associated integral transform”, Comm. Pure Appl. Math., 16 (1961), 187–214 | DOI | MR