A new mathematical framework finally solves the 'infinite energy' paradox that has plagued the physics of point particles for decades.
March 31, 2026
Original Paper
Homothetic Hodge$-$de Rham Theory and a Geometric Regularization of Elliptic Boundary Value Problems
arXiv · 2603.27564
The Takeaway
In standard physics, treating a particle like an electron as a 'point' leads to the impossible result that it has infinite electric energy at its center. By using a new type of 'homothetic' geometry, researchers smoothed out the math to allow for point-like particles with finite, realistic energy without breaking classical field laws.
From the abstract
We introduce a homothetic extension of classical Weyl integrable geometry by generalizing the usual linear gauge transformations to affine homothetic transformations centered at a distinguished harmonic, scale-invariant form $\alpha_d$. After relinearizing these affine gauge transformations via a suitable shift of variables, we obtain a twisted exterior calculus that is structurally equivalent to the Witten deformation of the de Rham complex. On this basis, we develop a corresponding homothetic