Computing light-front wave functions without light-front quantization : a large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small k$^{+}$ modes have been effectively "integrated out," with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function

Large deviation for small noise path-dependent stochastic differential equations

In this paper, we study the asymptotic behavior of randomly perturbed path-dependent stochastic differential equations with small parameter $\vartheta_{\varepsilon}$, when $\varepsilon \rightarrow 0$, $\vartheta_\varepsilon$ goes to $0$. When $\varepsilon \rightarrow 0$, we establish large deviation principle. The proof of the results relies on the weak convergence approach. As an application, we establish the large deviation for functionals of path-dependent SDEs in small time intervals.Comment: 12 page

Momentum-current gravitational multipoles of hadrons

We study multipole expansion of the momentum currents in hadrons with three series $S^{(J)}, \tilde{T}^{(J)}$ and $T^{(J)}$ in connection with the gravitational fields generated nearby. The momentum currents are related to their energy-momentum form factors, which in principle can be probed through processes like the deeply virtual Compton scattering currently studied at the Jefferson Lab 12 GeV facility and future Electron-Ion Collider. We define the leading momentum-current multipoles [the "tensor monopole" $\tau$ (T0) and "scalar quadrupole" $\hat{\sigma} ^{ij}$ (S2) moments], relating the former to the so-called D term in the literature. We calculate the momentum-current distribution in the hydrogen atom and its monopole moment in the basic unit of $\tau_{0} = \hslash^{2} / 4m_{e}$, showing that the sign of the D term has little to do with mechanical stability. The momentum-current distribution also strongly modifies the static gravitational field inside hadrons

Momentum-current gravitational multipoles of hadrons

We study multipole expansion of the momentum currents in hadrons with three series $S^{(J)}, \tilde{T}^{(J)}$ and $T^{(J)}$ in connection with the gravitational fields generated nearby. The momentum currents are related to their energy-momentum form factors, which in principle can be probed through processes like the deeply virtual Compton scattering currently studied at the Jefferson Lab 12 GeV facility and future Electron-Ion Collider. We define the leading momentum-current multipoles [the "tensor monopole" $\tau$ (T0) and "scalar quadrupole" $\hat{\sigma} ^{ij}$ (S2) moments], relating the former to the so-called D term in the literature. We calculate the momentum-current distribution in the hydrogen atom and its monopole moment in the basic unit of $\tau_{0} = \hslash^{2} / 4m_{e}$, showing that the sign of the D term has little to do with mechanical stability. The momentum-current distribution also strongly modifies the static gravitational field inside hadrons

THE APPLICATION OF PLANTAR PRESSURE MEASURING SYSTEM ON DESIGNING THE INDIVIDUATION INSOLE

The purpose of this study is to help the athlete prevent injuries and improve performance by deVising the individual insoles according to the plantar pressure measuring data. To stipulate the different movements in the different regions of the foot, the Footscan software compares the pressures during certain periods in the foot roll off. The dynamic region system detects the different parts of the foot (hallux, other toes, the different metatarsals, the midfoot, the medial and lateral heel). For each area the pressures, the ground contact and the contact time will be calculated. When all these data are collected, the Footscan software will interpret the data and give a proposal for a dynamic three dimension (030) correction ,insol'e and the modules which have to be used