The complexities of nonperturbative computations

The paper studies the behavior of equations of motions of Green’s functions under different running coupling constants in strongly coupled gauge field theories in terms of the Kolmogorov complexity

Riemann-Hilbert problem and quantum field theory: integrable renormalization, Dyson-Schwinger equations

In the first purpose, we concentrate on the theory of quantum integrable systems underlying the Connes-Kreimer approach. We introduce a new family of Hamiltonian systems depended on the perturbative renormalization process in renormalizable theories. It is observed that the renormalization group can determine an infinite dimensional integrable system such that this fact provides a link between this proposed class of motion integrals and renormalization flow. Moreover, with help of the integral renormalization theorems, we study motion integrals underlying Bogoliubv character and BCH series to obtain a new family of fixed point equations. In the second goal, we consider the combinatorics of Connes-Marcolli approach to provide a Hall rooted tree type reformulation from one particular object in this theory namely, universal Hopf algebra of renormalization $H_{\mathbb{U}}$. As the consequences, interesting relations between this Hopf algebra and some well-known combinatorial Hopf algebras are obtained and also, one can make a new Hall polynomial representation from universal singular frame such that based on the universal nature of this special loop, one can expect a Hall tree type scattering formula for physical information such as counterterms. In the third aim, with attention to the given rooted tree version of $H_{\mathbb{U}}$ and by applying the Connes-Marcolli's universal investigation, we discover a new geometric explanation from Dyson-Schwinger equations

From Dyson-Schwinger equations to the Riemann-Hilbert correspondence

In this paper, with the study of combinatorial Dyson–Schwinger equations at the level of the universal Hopf algebra of renormalization and with the extension of the universality of this specific Hopf algebra and also category of flat equisingular vector bundles to the level of these equations, we are going to consider the notion of a geometric description from nonperturbative theory

Formal aspects of non-perturbative quantum field theory via an operator theoretic setting

The paper builds the original foundations of a new operator theoretic setting for the study of quantum dynamics of non-perturbative aspects originated from Green’s functions in Quantum Field Theory with strong couplings

Non-perturbative \beta-functions via Feynman graphons

We show the existence of a new class of β-functions which can govern the running of strong coupling constants in gauge field theories

Can the Accuracy of Home Blood Glucose Monitors be affected by the Received Signal Strength of 900 MHz GSM Mobile Phones?

Background: People who use home blood glucose monitors may use their mobile phones in the close vicinity of medical devices. This study is aimed at investigating the effect of the signal strength of 900 MHz GSM mobile phones on the accuracy of home blood glucose monitors. Methods: Sixty non-diabetic volunteer individuals aged 21 - 28 years participated in this study. Blood samples were analyzed for glucose level by using a common blood glucose monitoring system. Each blood sample was analyzed twice, within ten minutes in presence and absence of electromagnetic fields generated by a common GSM mobile phone during ringing. Blood samples were divided into 3 groups of 20 samples each. Group 1: exposure to mobile phone radiation with weak signal strength. Group2: exposure to mobile phone radiation with strong signal strength. Group3: exposure to a switched–on mobile phone with no signal strength. Results: The magnitude of the changes in the first, second and third group between glucose levels of two measurements (׀ΔC׀ (were 7.4±3.9 mg/dl, 10.2±4.5 mg/ dl, 8.7±8.4 mg/dl respectively. The difference in the magnitude of the changes between the 1st and the 3rd groups was not statistically significant. Furthermore, the difference in the magnitude of the changes between the 2nd and the 3rd groups was not statistically significant. Conclusion: Findings of this study showed that the signal strength of 900 MHz GSM mobile phones cannot play a significant role in changing the accuracy of home blood glucose monitors