International Journal of Modern Physics A

Baryogenesis in the context of the compact $SU{(3)}_C\otimes SU{(4)}_L\otimes U{(1)}_X$ model is investigated. Using the finite temperature effective potential approach together with unitarity, stability and no ghost masses constraints, the existence of a strong first-order electroweak phase transition (EWPT) was shown and checked numerically during all steps of the spontaneous breakdown of the gauge symmetry of the model. Higgs masses regions fulfilling the EWPT criteria are also discussed. Moreover, and as a byproduct of our study, the $B$-violation via sphaleron was also emphasized.

In this paper, we have considered flat Friedmann–Robertson–Walker (FRW) model of the universe and reviewed the modified Chaplygin gas as the fluid source. Associated with the scalar field model, we have determined the Hubble parameter as a generating function in terms of the scalar field. Instead of hyperbolic function, we have taken Jacobi elliptic function and Abel function in the generating function and obtained modified Chaplygin–Jacobi gas (MCJG) and modified Chaplygin–Abel gas (MCAG) equation of states, respectively. Next, we have assumed that the universe is filled in dark matter, radiation, and dark energy. The sources of dark energy candidates are assumed as MCJG and MCAG. We have constrained the model parameters by recent observational data analysis. Using ${\chi }^2$ minimum test (maximum likelihood estimation), we have determined the best-fit values of the model parameters by OHD$+$CMB$+$BAO$+$SNIa joint data analysis. To examine the viability of the MCJG and MCAG models, we have determined the values of the deviations of information criteria like △AIC, △BIC and △DIC. The evolutions of cosmological and cosmographical parameters (like equation of state, deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studied for our best-fit values of model parameters. To check the classical stability of the models, we have examined the values of square speed of sound $v_s^2$ in the interval $(0,1)$ for expansion of the universe.

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking is predetermined by confinement. It is shown that CCL retains all basic relations of the standard chiral theory but enables one to include quark degrees of freedom in the CCL. The expansion of the CCL provides the Gell–Mann–Oakes–Renner (GMOR) relations and the masses and decay constants of all chiral mesons, including $\eta ,{\eta }^{\prime }$. For the latter, one needs to define a nonchiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with the experimental and lattice data.

In this paper, we solve the quaternionic Dirac equation $(ℍ\mathrm{\text{DE}})$ in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation $(ℂ\mathrm{\text{DE}})$. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory $(ℍ\mathrm{\text{QFT}})$.

In this paper, we present an exact solution of the Klein–Gordon equation in the framework of the fractional-dimensional space, in which the momentum and position operators satisfying the $R$-deformed Heisenberg algebras. Accordingly, three essential problems have been solved such as: the free Klein–Gordon equation, the Klein–Gordon equation with mixed scalar and vector linear potentials and with mixed scalar and vector inversely linear potentials of Coulomb-type. For all these considered cases, the expressions of the eigenfunctions are determined and expressed in terms of the special functions: the Bessel functions of the first kind for the free case, the biconfluent Heun functions for the second case and the confluent hypergeometric functions for the end case, and the corresponding eigenvalues are exactly obtained.

In this work, we carry out a study of the conserved quantities and dynamical structure of the four-dimensional modified axion electrodynamics theory described by the axion-photon coupling. In the first part of the analysis, we employ the covariant phase space method to construct the conserved currents and to derive the Noether charges associated with the gauge symmetry of the theory. We further derive the improved energy–momentum tensor using the Belinfante–Rosenfeld procedure, which leads us to the expressions for the energy, momentum, and energy flux densities. Thereafter, with the help of Faddeev–Jackiw’s Hamiltonian reduction formalism, we obtain the relevant fundamental brackets structure for the dynamic variables and the functional measure for determining the quantum transition amplitude. We also confirm that modified axion electrodynamics has three physical degrees of freedom per space point. Moreover, using this symplectic framework, we yield the gauge transformations and the structure of the constraints directly from the zero-modes of the corresponding pre-symplectic matrix.

Within the framework of the recently proposed Taylor–Lagrange regularization scheme which leads to finite elementary amplitudes in four-dimensional space–time with no additional dimensionful scales — we show that the trace of the energy–momentum tensor does not show any anomalous contribution even though quantum corrections are considered. Moreover, since the only renormalization we can think of within this scheme is a finite renormalization of the bare parameters to give the physical ones, the canonical dimension of quantum fields is also preserved by the use of this regularization scheme.