Fundamental length hypothesis in a Gauge theory context

  • Vladimir G. Kadyshevsky
Fiber Bundles and Extended Particle Structures
Part of the Lecture Notes in Physics book series (LNP, volume 94)


The new gauge formulation of the electromagnetic interaction theory, containing the “fundamental length” ℓ as a universal scale like ħ and c, is worked out. A key part belongs to the 4-dimensional de Sitter p-space, with the curvature radius ħ/ℓc In the new approach the electromagnetic potential becomes a 5-vector associated with de Sitter group O(4.1). The extra fifth component, called the τ-photon, similar to scalar and longitudinal photons, does not correspond to an independent dynamical degree of freedom. Respectively, the new local gauge group is larger than the ordinary one and depends intrinsically on the fundamental length ℓ

The gauge invariant equations of motion, replacing the Dirac-Maxwell equations, are set up. The new formulation is minimal with respect to the 5-potential but is not so in terms of the usual 4-potential.As a result, the underlying physics looks much richer than the ordinary electromagnetic phenomena. The new scheme predicts the existence of the electric dipole moments for charged particles, leading to a direct violation of P- and CP-symmetries, and the new universal correction to the (g-2)-anomaly. Further, some new group of internal symmetry, SUτ(2), arises that can be used to describe the lie-symmetry of the electromagnetic interactions. It turns out that SUτ(2)-symmetry is violated by the 4-fermion type interaction, induced by τ-photons, with associated coupling constant ≈αℓ2. This novel interaction might give rise to the μe-mass difference and processes like μ → 3e, μ → eγ, etc.

In the limit ℓ → 0, the new field equations turn into the Dirac-Maxwell equations for the electron, muon and electromagnetic fields. So, one may consider this approach as a generalization in a profound way of the standard theory of electromagnetic interactions at small distances ≲ℓ (high energies ≲ 1/ℓ).

The upper bound for the fundamental length l is discussed taking into account the various experimental data.


Electric Dipole Moment Electromagnetic Interaction Parity Violation Magnetic Dipole Moment Fundamental Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Vladimir G. Kadyshevsky
    • 1
  1. 1.Fermi National Accelerator LaboratoryBatavia

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