We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost and the ge
neral solution is not translationally invariant in the radial coordinate. However, under the approximation that the fermion is completely dragged by the vortical motion, valid for large angular velocities, translation invariance is recovered. The propagator can then be written in momentum space. The result is suited to be used applying ordinary Feynman rules for perturbative calculations in momentum space.
The $SU(3)$ gauge-field propagators computed from the lattice have been exhaustively used in the investigation of the low-momentum dynamics of QCD, in a judicious interplay with results from other nonperturbative approaches, and for the extraction of
fundamental parameters of QCD like $Lambda_{overline{rm MS}}$ as well. The impact of the discretization artifacts and their role in the extrapolation of the results to the continuum limit have not been fully understood so far. We report here about a very careful analysis of the physical scaling violation of the Landau-gauge propagators renormalized in MOM scheme and the Taylor coupling, steering us towards an insightful understanding of the effects from discretization artifacts which makes therefore possible a reliable continuum-limit extrapolation.
For the flavor-singlet heavy quark system of bottomonia, we compute the masses of the ground state mesons in four different channels, namely, pseudo-scalar ($eta_{b}(1S)$), vector ($Upsilon(1S)$), scalar ($chi_{b_0}(1P)$) and axial vector ($chi_{b_{1
}}(1P)$). We also calculate the weak decay constants of the $eta_{b}(1S)$ and $Upsilon(1S)$ as well as the charge radius of $eta_{b}(1S)$. It complements our previous study of the corresponding charmonia systems: $eta_c(1S)$, $J/Psi(1S)$, $chi_{c_0}(1P)$) and ($chi_{c_{1}}(1P)$). The unified formalism for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$times$vector contact interaction. Whenever a comparison is possible, our results are in fairly good agreement with experimental data and model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations involving sophisticated interaction kernels. Within the same framework, we also report the elastic and transition form factors to two photons for the pseudo-scalar channels $eta_{c}(1S)$ and $eta_{b}(1S)$ in addition to the elastic form factors for the vector mesons $J/Psi$ and $Upsilon$ for a wide range of photon momentum transfer squared ($Q^2$). For $eta_{c}(1S)$ and $eta_{b}(1S)$, we also provide predictions of an algebraic model which correlates remarkably well between the known infrared and ultraviolet limits of these form factors.
We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action generates complex dynamics in the weak-lasing domai
n way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak dis- tributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot noise arising from the influx of polaritons. That results in a complex inhomo- geneous line broadening.
Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of th
at equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion--gauge-boson vertex is an important factor in deciding the issue.
