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.
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