Mathematical Physics

2607 Submissions

[3] viXra:2607.0066 [pdf] submitted on 2026-07-15 22:26:14

Dual Architecture in Yang-mills Theory: Algebraic Regularization, Wightman Axioms, and Mass Gap

Authors: Julinho Jorge Luís
Comments: 35 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This article presents the Dual Architecture, an algebraic regularization method for divergent integrals in quantum field theory. The method rests on two functions defined over complementary domains: the Euler integral for the Gamma function over the positive real axis, and a companion integral over the negative real axis. When one integral representation diverges, its dual converges, and the regularized value is taken as the reciprocal of the convergent one. The sign alternation is encoded by an entire function without zeros on the negative real axis. Applied to Yang-Mills theory with gauge group SU(N), the method demonstrates the existence of a mass gap persisting to all orders of perturbation theory. The perturbative series of the Dual Architecture converges absolutely because the regularized Gamma values at negative integers decay factorially, in contrast to the factorial growth of the traditional Dyson series. Evidence for the proposal comes from two independent anomalies that the established method leaves unexplained. The first is a residual error in the WKB expansion of the quartic anharmonic oscillator, computed numerically to high order and documented in the literature. The second is the sign of the vacuum energy density, which the traditional analytic continuation yields as negative, contradicting the observed accelerated expansion of the Universe. The Dual Architecture corrects both anomalies, and they share a common origin in the same negative half-integer argument of the Gamma function. The method eliminates the renormalization scale because integrals are evaluated directly in four dimensions, producing finite values without pole subtraction. Correspondence with quantum electrodynamics at one loop is verified. The Wightman axioms are satisfied.
Category: Mathematical Physics

[2] viXra:2607.0057 [pdf] submitted on 2026-07-14 13:25:35

Some Remarks on the Riemann Hypothesis, Concerning the Zero-Finding Theorem II

Authors: Holger Döring
Comments: 22 Pages.

At first, this second description also is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical, more physical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory.
Category: Mathematical Physics

[1] viXra:2607.0027 [pdf] submitted on 2026-07-08 20:58:45

Some Short Remarks on the Riemannian Hypothesis, Concerning the Zero-Finding Theorem

Authors: Holger Döring
Comments: 3 Pages. In German

At first, this description is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory. A more detailed paper will follow.
Category: Mathematical Physics