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The role of Pythagorean prime 137 in octonion Dirac’s equation in spacetime lattice and its links to the fine structure constant and the golden angle

Jau Tang, Brian Tang

In this work, we present a theory to link the fine structure constant
α to the Pythagorean prime 137. This model is based on quantized
lattice spacetime and gauge symmetry of electromagnetism. Unlike
the conventional Dirac equation which assumes an electron as a
point-like particle without an internal structure. However, such a
concept would lead to a divergence in self-energy. Instead, we treat
an electron as a charged particle with an internal structure and a
finite size due to the self’s electrostatic interaction. We propose a
modified equation using Cayley-Dickson’s octonion operators of the
Clifford geometric algebra formalism. We elucidate the number
theory of the magic 137 as a Pythagorean prime triple with


 
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