Calculus, Gauge Theory and Noncommutative Worlds

@article{Kauffman2022CalculusGT,
  title={Calculus, Gauge Theory and Noncommutative Worlds},
  author={Louis H. Kauffman},
  journal={Symmetry},
  year={2022},
  volume={14},
  pages={430}
}
This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generalizations of electromagnetism that are related to gauge theory and with the early work of Hermann Weyl. The territory here explored is self-contained mathematically. It is elementary, algebraic, and subject to possible generalizations that are discussed in the… 

References

SHOWING 1-10 OF 43 REFERENCES

Feynman’s proof of the Maxwell equations

Feynman’s proof of the Maxwell equations, discovered in 1948 but never published, is here put on record, together with some editorial comments to put the proof into its historical context.

Aberration and the Speed of Gravity

Differential geometry in noncommutative worlds, in “Quantum Gravity”, ed

  • 2000

Space-Time-Matter

On Feynman’s proof of the Maxwell equations

Feynman’s proof, as recounted by F. J. Dyson [Am. J. Phys. 58, 209–211 (1990)], that the Lorentz force law and two of Maxwell’s equations can apparently be deduced from minimal assumptions about the

Minimal Coupling and Feynman’s

  • Proof. International Journal of Theoretical Physics
  • 1999

Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

The canonical structure of a reparametrization invariant Lagrangian for an extended object embedded in a bulk space M is shown to lead to some familiar Lagrangians, such as the relativistic point particle in an electromagnetic field, the string theory Lagrangia, and the Dirac-Nambu-Goto Lagrangi.

The Dawning of Gauge Theory

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known

An Elementary Primer for Gauge Theory

Gauge theory is now recognized as one of the most revolutionary discoveries in physics since the development of quantum mechanics. This primer explains how and why gauge theory has dramatically