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Can the Lorentz symmetry supply something that is supplied by the gauge symmetry?
At the foundation of modern physics lie two symmetries: the Lorentz symmetry
and the gauge symmetry, which play quite different roles in the establishment
of the standard model. In this paper, it is shown that, different from what is
usually expected, the two symmetries, although mathematically independent of
each other, have important overlap in their physical effects. Specifically, we
find that the interaction Lagrangian of QED can be "derived", based on the
Lorentz symmetry with some auxiliary assumption about vacuum fluctuations,
without resorting to the gauge symmetry. In particular, the derivation is based
on geometric relations among representation spaces of the SL(2,C) group. In
this formulation of the interaction Lagrangian, the origin of the topological
equivalence of the eight basic Feynman diagrams in QED can be seen quite
clearly.Comment: 18 pages, no figur
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