Modern Physics Letters A

I discuss the momentum and angular momentum decomposition problem in the Abelian Higgs model. The usual gauge-invariant extension (GIE) construction is incorporated naturally into the framework of quantum gauge transformation à la Strocchi and Wightman and with this, I investigate the momentum and angular momentum separation in a class of GIE conditions which correspond to the so-called “static gauges”. Using this language, I find that the so-called “generator criterion” does not generally hold even for the dressed physical field. In the case of U(1) symmetry breaking, I generalize the standard GIE construction to include the matter field degrees of freedom so that the usual separation pattern of momentum and angular momentum in the unitarity gauge can be incorporated into the same universal framework. When the static gauge condition could not uniquely fix the gauge, I show that this GIE construction should be expanded to take into account the residual gauge symmetry. In some cases, I reveal that the usual momentum or angular momentum separation pattern in terms of the physical dressed field variables needs some type of modification due to the nontrivial commutator structure of the underlying quantum gauge choice. Finally, I give some remarks on the general GIE constructions in connection with the possible commutator issues and modification of momentum and angular momentum separation patterns.

Recently, we have proposed a quark mass matrix model based on U(3) × U(3)${}^{\prime }$ family symmetry, in which up- and down-quark mass matrices $M_u$ and $M_d$ are described only by complex parameters $a_u$ and $a_d$, respectively. When we use charged lepton masses as additional input values, we can successfully obtain predictions for quark masses and Cabibbo–Kobayashi–Maskawa mixing. Since we have only one complex parameter $a_q$ for each mass matrix $M_q$, we can obtain a parameter-independent mass relation by using three equations for $\mathrm{\text{Tr}}[H_q]$, $\mathrm{\text{Tr}}[H_q{H}_q]$ and $\mathrm{\text{det}}{H}_q$, where $H_q\equiv M_q{M}_q^{†}$ ($q=u,d$). In this paper, we investigate the parameter-independent feature of the quark mass relation in the model.

In this paper, our main aim is to obtain the transmission (T) and the reflection (R) coefficients for one-dimensional scattering state of the spin-$\frac{1}{2}$ particles in an interaction with a special nuclear potential. For this reason, at first, we consider Dirac equation and then obtain the Milne’s nonlinear differential equation due to minimal length from Schrödinger-like equation and then calculate the T- and R-coefficients using one-dimensional Woods–Saxon potential on the basis of the generalized uncertainty principle. Finally, we will check the validity and the correctness of our results.

Based on the two flavor Nambu–Jona-Lasinio (NJL) model with a proper time regularization, we used stationary wave condition (SWC) for the first time to study the influence of the finite volume effects on the chiral phase transition of quark matter at finite temperature. It is found that when the cubic volume size $L$ is larger than $L_{max}^{\mathrm{\text{SWC}}}=500$ fm, the chiral quark condensate is indistinguishable from that at $L=\infty$. Here, it should be noted that 500 fm is far greater than the size of QGP produced at laboratory and the lattice QCD simulation space size. It is also much larger than the previous limit size $L_{max}^{\mathrm{\text{APBC}}}=5$ fm estimated by the commonly used anti-periodic boundary condition (APBC). We also found that when the space size $L$ is less than $L_{min}^{\mathrm{\text{SWC}}}=0.25$ fm, the spontaneous symmetry breaking concept is no longer valid. In addition, we first introduce the spatial susceptibility, and through the study of the spatial susceptibility, it was revealed for the first time that the chiral phase transition caused by the finite volume effects in the non-chiral limit is a crossover.

In this work, control rod worth, xenon (Xe) effect on reactivity and power defect have been measured by doing experiments in the BAEC TRIGA Mark-II research reactor (BTRR) and through established theoretical analysis. Firstly, to study the xenon-135 effect on reactivity, reactor is critical at 2.4 MW for several hours. Next, experiments have been performed at very low power (50 W) to avoid temperature effects. Moreover, for the power defect experiment, different increasing power level has been tested by withdrawing the control rods. Finally, it is concluded that the total control rods worth of the BAEC TRIGA Mark-II research reactor, as determined through this study, is enough to run the reactor at full power (3 MW) considering the xenon-135 and fuel temperature effects.

The models of $f(R,T)$ gravity are efficient in describing a non-minimal coupling between geometry and matter. In this paper, the extended theory of gravity describes the non-minimal coupling between matter and geometry using special cosmological model of $f(R,T)=f_1(R)+f_2(R)f_3(T)$ in Bianchi-V spacetime; whose functional relations are $f_1(R)=f_2(R)=R$ and $f_3(T)=\beta T$, where $\beta$ is a constant. The Einstein’s field equation has been solved by taking special choice of scale factor as $a={\{t^{m}exp(\lambda t)\}}^{\frac{1}{n}}$, where $m$, $\lambda$ and $n$ are constants. The energy and other stability conditions obtained in this paper explain the physical behavior of phase transition of universe and it also confirms the stability of the derived model.