International Journal of Modern Physics A

In this paper, we continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum space. The natural place to start are the famous banana diagrams, which we explore in this paper. In position space, these are just products of n propagators. First, we explain that these functions satisfy an equation of order $2^n$. These should be compared with Picard–Fuchs equations derived for the momentum space integral. We find that the Fourier transform of the position space operator contains the Picard–Fuchs one as a rightmost factor. The order of these operators is a special issue, especially since the order in momentum space is governed by degree in x in position space. For the generic mass case, this factorization pattern is complicated and it seems like the order of the Fourier transformed position space operators is much bigger than that of the Picard–Fuchs. Furthermore, one may ask what happens if after factorization we take the Picard–Fuchs operators back into position space. We discover that the result is again factorized, with the rightmost factor being the original position space equation. We demonstrate how this works in examples and discuss implications for more sophisticated Feynman integrals.

Bright transient objects in different wave bands have been discovered in recent years. To explain these short (from ms to s), and very powerful events, different models, galactic and extragalactic, have been considered. One of the popular models is based on the suggestion of transformation of the magnetized plasma blob, presumably a magnetohydrodynamic (MHD) shock wave, moving with relativistic speed, into electromagnetic (EM) pulse after collision with some obstacle, or entering into media with different properties. Such transformation cannot be described in the frame of classical MHD equations, which don’t contain the displacement current and don’t include such transformation. Updating of the classic MHD equations by using of full set of Maxwell equations with displacement current, made recently by several authors, gave a possibility to describe hydrodynamic phenomena, together with electromagnetic ones by the same set of equations. Here we apply these equations for study of propagation of different waves with account of displacement current, and of transformation between different kinds of waves in the nonuniform media. We derive a dispersion equation describing a propagation of a weak linear wave in a uniform magnetized plasma, and consider in detail the cases with perpendicular and parallel motion to the magnetic field. It contains MHD, HD, Alfven and EM waves in the limiting cases, and some new types of behavior in a general situation. We consider a plasma with zero viscosity and heat conductivity, with a finite scalar electric conductivity. We have shown that the transformation of MHD into EM wave may happen only in a highly magnetized plasma, and have found the region of parameters, where no waves exist and only damping static perturbations may be present.

In this paper, we construct a deformed Schwarzschild black hole from the de Sitter gauge theory of gravity within Dunkl generalization and we determine the metric coefficients versus Dunkl parameter and parity operators. Since the spacetime coordinates are not affected by the group transformations, only fields are allowed to change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed as well. Additionally, we analyze the modifications on the thermodynamic properties to a spherically symmetric black hole due to Dunkl parameters for even and odd parities. Finally, we verify a novel remark highlighted from heat capacity: the appearance of a phase transition when the odd parity is taken into account.

The pursuit for the genuine fundamental description, governing nature at some high-energy scale, must invariably consider the yet-unknown mechanism behind the generation of neutrino mass. Lepton-flavor violating decays $l_{\alpha }\to l_{\beta }\gamma$, allowed in the presence of neutrino mass and mixing, provide a mean to look for physics beyond the Standard Model. In this work, we consider the inverse seesaw mechanism (ISS) and then revisit the calculation of its contributions to the branching ratios of the aforementioned decay processes. Our analytic results are consistent, as they are gauge invariant, gauge independent, ultraviolet finite, and of decoupling nature. Among the decays $l_{\alpha }\to l_{\beta }\gamma$, we find $\mu \to \gamma e$ to be the most promising, in the light of current bounds by the MEG Collaboration. Deviations from unitarity in the mixing of light neutrinos are related to the branching ratios $\mathrm{\text{Br}}\left(\right.l_{\alpha }\to \gamma l_{\beta }\left)\right.$ in a simple manner, which we address, then finding that the constraints on non-unitarity effects from MEG data will be improved by the upcoming MEG II update by a factor $\sim \frac{1}{3}$.

This work examines whether evolving wormhole solution is possible or not in $f(R,T)$ modified gravity theory. In the background of inhomogeneous FLRW-type wormhole configuration, the field equations are investigated for different choices of scale factors and shape functions. For the power law and exponential choice of the scale factor from cosmological context and decoupled power law of $f(R,T)$ in each variable, wormhole configuration has been examined for two viable choices of shape function. Energy conditions are examined graphically for a range of values of the parameters involved. Finally, the possibility of emergent scenario at early cosmic evolution has been examined.

Triply Special Relativity is a deformation of Special Relativity based on three fundamental parameters that describes a noncommutative geometry on a curved space–time, preserving the Lorentz invariance and the principle of relativity. Its symmetries are generated by a 14-parameter nonlinear algebra. In this paper, we discuss a generalization of the original model and construct its realizations on a canonical phase space. We also investigate in more detail its classical limit, obtained by replacing the commutators by Poisson brackets.