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| viXra.org > Mathematical Physics > 2607 |
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[5] viXra:2607.0095 [pdf] submitted on 2026-07-24 00:38:13
Authors: Jaykov Foukzon
Comments: 24 Pages.
In this paper, we show how the finite formulation of quantum field theorybased on Langevin equations can be generalized to the case of nonrenormalizabletheories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu,is put in a path-integral form in [5]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of the vacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}²u207f,n≥2,d≥4 model quantum field theory in Minkowski spacetime is considered.
Category: Mathematical Physics
[4] viXra:2607.0093 [pdf] submitted on 2026-07-24 13:25:00
Authors: Frederic Lassiaille
Comments: 9 Pages.
We present the solution to the Yang-Mills existence and mass gap problem by incorporating full General Relativity into Quantum Field Theory via its surrounding equation. By replacing the idealized single-source, asymptotically flat approximation with a multi-source surrounding energy distribution vector Dμ(x), the local field operator calibration is dynamically governed through the purely algebraic structure of the global background environment via the scale-invariant ratio v/c. We show that this ratio possesses an intrinsic scale invariance property under global energy rescalings λ ∈ ℝ*, preventing field configurations from collapsing into zero-energy or infinitesimal states. In low-density vacuum environments, the surrounding background dynamically amplifies the effective gauge interaction energy in inverse proportion to the background density, guaranteeing a strictly positive mass gap Δ > 0. Furthermore, at high energy scales and short distances, the accumulation of local surrounding energy in Dμ(x) induces an intrinsic saturation of the v/c ratio, dynamically damping high-momentum interaction amplitudes and providing a non-perturbative UV regularization scheme without ad hoc cutoffs or counterterm subtractions. This algebraic embedding links full relativistic background constraints directly to the resolution of fundamental open problems in subatomic quantum field theory.
Category: Mathematical Physics
[3] viXra:2607.0066 [pdf] submitted on 2026-07-15 22:26:14
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
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
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
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