Yang-mills theory to Electromagnetic Force
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Abstract
This research explores the photon (γ) as the gauge boson responsible for mediating the electromagnetic force, framed within Yang–Mills gauge field theory. The work investigates how U(1) gauge symmetry naturally gives rise to the electromagnetic field and explains the masslessness, spin-1 nature, and non-self-interaction of the photon as direct consequences of unbroken gauge invariance.
Through comparative analysis between Abelian and non-Abelian gauge theories, the study demonstrates that while Yang–Mills fields (SU(2), SU(3)) yield self-interacting gauge bosons, the Abelian U(1) symmetry of electromagnetism produces a linear, non-self-interacting field—the classical Maxwell equations emerging as a special case.
The findings confirm that the photon’s existence and properties are not empirical accidents but logical necessities of gauge principles. Ultimately, this project underscores the profound unity between electromagnetism and the broader framework of modern gauge theory, situating the photon as a fundamental manifestation of symmetry in nature.
Through comparative analysis between Abelian and non-Abelian gauge theories, the study demonstrates that while Yang–Mills fields (SU(2), SU(3)) yield self-interacting gauge bosons, the Abelian U(1) symmetry of electromagnetism produces a linear, non-self-interacting field—the classical Maxwell equations emerging as a special case.
The findings confirm that the photon’s existence and properties are not empirical accidents but logical necessities of gauge principles. Ultimately, this project underscores the profound unity between electromagnetism and the broader framework of modern gauge theory, situating the photon as a fundamental manifestation of symmetry in nature.
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