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Journal of Pure and Applied Mathematics

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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

Author(s): Jau Tang* and 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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Citations : 7299

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