On Gauge Freedom and Interactions

The notion of gauge freedom is discussed in the context of the 2-spinor approach to Maxwell-Dirac fields. The various types of boson interaction terms arising in a generic gauge field theory are laid down, and detailed in the particular case of gauge boson interactions in the electroweak theory. Finally, several observations of ‘philosophical nature’ are offered, together with some ideas for future work.

Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

Lorentz violating gaugeon formalism of Yang–Mills theory

VSR is a way of keeping the main relativistic effects intact using subgroups of the Lorentz group instead of the full Lorentz group itself. In this paper, we study the quantization of the Yang–Mills theory, gaugeon formalism within the VSR framework. The gauge freedom is restored once we develop the gaugeon formalism. Also, the mass of corresponding gauge boson is modified because of the VSR effect. We find that the gaugeon formalism for Yang–Mills theory in VSR is consistent with the Lorentz invariant case except the fact that each field gets mass. We also discuss the generalization of BRST transformation within VSR framework. It is found that the gaugeon modes appear in the configuration space through the Jacobian of functional measure.

Electromagnetic spin creates torsion

It is shown the intrinsic spin, and only the spin, of the electromagnetic field creates torsion. The struggle raged for decades: How to reconcile the facts that photons have spin, but minimal coupling breaks gauge invariance and therefore must be abandoned, leaving us with the unphysical situation in which spin does not create torsion. By generalizing the gauge freedom of the torsion field, a covariant, gauge-invariant description is found whereby the electromagnetic spin creates a torsion field. In fact, it is shown if electromagnetic gauge invariance holds, torsion must be present.

Maxwell's Equations, Stokes' Theorem, and the Conservation of Charge

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields DH to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and $\emVec{A}$ do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of DH we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.