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arXiv · 1404.5131

Charge quantization emerging from irreducible representations of the gauge group U(1) and local gauge invariance in 2-spinor lenguage

J. Buitrago
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Abstract

A new classical 2-spinor approach to $U(1)$ gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a $U(1)$ local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representations condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials.

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J. Buitrago. 2014-06-03. Charge quantization emerging from irreducible representations of the gauge group U(1) and local gauge invariance in 2-spinor lenguage. https://arxiv.org/abs/1404.5131

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