International Journal of Modern Physics A

We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formalism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which satisfy 32 coupled equations. For massless fermions, the number of independent equations can be significantly reduced due to the decoupling of left-handed and right-handed particles. It can be proved that out of many components of Wigner functions and their coupled equations, only one kinetic equation for the distribution function is independent. This is called the disentanglement theorem for Wigner functions of chiral fermions. For massive fermions, it turns out that one particle distribution function and three spin distribution functions are independent and satisfy four kinetic equations. Various chiral and spin effects such as chiral magnetic and vortical effects, the chiral separation effect, spin polarization effects can be consistently described in the formalism.

We evaluate the quantum expectation values in nonsimply connected spaces by using UV improved Green’s functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green’s functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.

In a primordial universe pre- (post-)inflationary era, there could be phases of early universe made of cold gas baryons, radiation and early post-inflationary cosmological constant. I showed that in the baryonic epoch, the quantum vacuum is unique. By using the standard quantization scheme for a massive minimally coupled scalar field with maximal conformal symmetry in the classical space–time, I demonstrated that the scalar modes had an effective mass $m_{\mathrm{\text{eff}}}^2\approx 0$ (or $m_{\mathrm{\text{eff}}}^2\approx \mathrm{\text{const}}$). This argument was validated when the conformal time $\eta$ kept so close to the inflation ending time $\eta ={\eta }_c$. The energy density of the baryonic matter diverged at the inflation border and vanishes at the late time future. Furthermore, I argued that at very early accelerating epoch when the radiation was the dominant part in the close competition with the early time cosmological constant, fine-tuned mass of the scalar field $m\propto \sqrt{\mathrm{\Lambda }}$ also provided a unique quantum vacuum. The reason is that the effective mass eventually is vanished. A remarkable observation was that all the other possible vacuum states “squeezed” eternally.

We solve the equations of motion of a complex ${\varphi }^4$ theory coupled to some given gauge field background. The solutions are given in both cylindrical and spherical coordinates and have finite energy.

This paper investigates the dynamics of spherical collapse in the framework of energy–momentum squared gravity. This theory overcomes the big-bang singularity and provides viable cosmological consequences in the early time universe. We proceed our work by considering the nonstatic spherically symmetric space–time in the interior and static spherically symmetric metric in the exterior regions of the star. The Darmois junction conditions between interior and exterior geometries are derived. We construct dynamical equations through the Misner–Sharp technique to analyze the impact of matter variables and dark source terms on the collapsing phenomenon. A correlation among dark source terms, Weyl scalar and matter variables is also established. Due to the presence of multivariate function and its derivatives, space–time is no longer considered to be conformally flat. To obtain conformally flat space–time, we have considered a particular model of this gravity which yields conformally flat space–time and homogeneity of the energy density through the entire system. We conclude that positive dark source terms as well as negative pressure gradient provide the anti-gravitational behavior leading to the stability of self-gravitating objects and hence prevent the collapsing process.

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in $3+1$ dimensions. For arbitrary wave $l\ne 0$, the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

We investigate the contributions of the Cartan generators in the static potentials for various representations in the framework of the domain model of center vortices for SU(3) gauge theory. Using the center domains with the cores corresponding to only one Cartan generator $H_8$, already given as a particular proposal, leads to some concavities in the potentials for higher representations. Furthermore, the string tension of the fundamental representation is the same at Casimir scaling and $N$-ality regimes. We add the contribution of the other Cartan generator $H_3$ to the potentials and therefore these shortcomings can be eliminated. However, we discuss that at intermediate range of distances the potentials induced by only $H_8$ agree with the Casimir scaling better than those corresponding to both Cartan generators.