International Journal of Modern Physics A

In this paper, we define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the quantum field theory. As an example, we consider the scalar field with $\frac{\lambda }{4!}{\mathrm{\Phi }}^4$ interaction. To the third-order of perturbation, we obtain the equation of motion of the dynamic expectation value of the scalar field in the defined state.

This paper explores the topic of relativistic particles with zero spins from a unique perspective. Our approach is derived from the Dunkl derivative, which we used to investigate this issue. By examining the ($1+1$)-dimensional DKP equation, we obtain eigenfunctions. Additionally, we replace the standard partial derivative with the Dunkl derivative and solve the relativistic particle problem in a box using the new formalism. We then determine the energy spectrum for this scenario. Following this, we investigate the scattering of the potential step problem and the Ramsauer–Townsend effect separately. Finally, we calculate the coefficients of transmission and reflection.

We readdress the issue of strong CP violation both in the Standard Model (SM) and in the Minimal Left–Right (LR) Symmetric Model and try to clear the confusion that seems to still pervade the field. We argue that the smallness of strong CP violation, while harmless and basically decoupled from the rest of the physics in the SM, in the context of LR symmetry provides a blessing by helping to narrow down the parameter space of the theory and connecting apparently the uncorrelated physical quantities. In particular, in the context of left–right symmetry being parity, it either points to the suppression of leptonic CP violation noticed before, or leads to relatively light right-handed neutrinos, potentially accessible at the next hadron collider. The latter, more natural in view of complex quark Yukawa couplings, goes hand in hand with the smallness of lepton flavor violation and enhances the possibility of observing neutrinoless double-beta decay.

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume $V\sim L^3$. A two-flavor Nambu–Jona-Lasinio model at finite temperature $T$ and chemical potential $\mu$ is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as $T$ increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit $V\to \infty$. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

In this paper, we construct the dispersionless coupled constrained KP hierarchy. We also introduce vital formal Laurent series ${{𝒴}}_{l,1},{{𝒴}}_{l,2}$ to construct new flows, which lead out the additional symmetries of the dispersionless coupled constrained KP hierarchy. The additional flows construct a sub-algebra of the Virasoro algebra. In addition, we give the additional flows acting on $\mu (t,\lambda ),\widehat{\mu }(t,\lambda )$ and $\rho (t,\lambda ),\widehat{\rho }(t,\lambda )$ of the dispersionless coupled constrained KP hierarchy.

Massive Klein–Gordon theory is quantized on the timelike hypercylinder in Minkowski space. Crucially, not only the propagating, but also the evanescent sector of phase space is included, laying in this way foundations for a quantum scattering theory of fields at finite distance. To achieve this, the novel $\alpha$-Kähler quantization scheme is employed in the framework of general boundary quantum field theory. A potential quantization ambiguity is fixed by stringent requirements, leading to a unitary radial evolution. Formulas for building scattering amplitudes and correlation functions are exhibited. A novel LSZ formula is derived, applicable to scattering at finite distance.

Motivated by recent progresses in experiments in searching for the ${\mathrm{\Omega }}_c$ baryons, we systematically analyze the strong decay behaviors of single heavy baryons ${\mathrm{\Lambda }}_Q$, ${\mathrm{\Sigma }}_Q$ and ${\mathrm{\Omega }}_Q$. The two-body strong decay properties of $S$-wave, $P$-wave and some $D$-wave states are studied with the ${}^3{P}_0$ model. The results support assigning the recently observed ${\mathrm{\Omega }}_c(3185)$ and ${\mathrm{\Omega }}_c(3327)$ as the 2S(${\frac{3}{2}}^{+}$) and 1D(${\frac{3}{2}}^{+}$) states, respectively. In addition, the quantum numbers of many other experimentally observed baryons are also suggested according to their strong decays. Finally, some baryons which have good potentials to be observed in experiments are predicted and the possible decay channels for searching for these predicted states are also suggested.

In this paper, we analyze the scattering process in a two-field model in $(1+1)$ dimensions, with the special property to have several topological solutions: (i) one with higher rest mass, characterized by a nested defect (lump inside a kink) and (ii) four others having lower rest mass, degenerated, and characterized by a kink inside kink. We investigate kink–antikink symmetric scattering, where the kink and antikink have higher rest mass and the same initial velocity modulus $v$. The output of scattering presents a wide range of behaviors, such as annihilation of the kink–antikink pair, the emission of radiation jets, the generation of oscillating pulses and the change of the topological sector. We show that the changing of the topological sector is favored, and only two of the four sectors are possible as outcomes. Moreover, despite the degeneracy in energy, the distribution of the final states is asymmetric in the phase space, being an effect of the presence of vibrational states.

We construct approximate solutions to the Einstein–Maxwell theory with uplifting the four-dimensional Fubini–Study Kähler manifold. We find the solutions can be expressed as the integrals of two special functions. The solutions are regular almost everywhere except a bolt structure on a single point in any dimensionality. We also show that in the context of considered ansatzes for the metric function and the Maxwell field, the solutions are unique and cannot be nontrivially extended to include the cosmological constant in any dimensions.

We examine a generalization of the usual self-duality equations for Yang–Mills theory when the color space admits a nontrivial involution. This involution allows us to construct a nontrivial twist which may be combined with the Hodge star to form a twisted self-dual curvature. We will construct a simple example of twisted self-duality for $su(2)\oplus su(2)$ gauge theory along with its explicit solutions, both in Euclidean and Minkowski backgrounds, and then dimensionally reduce from four dimensions to obtain families of nontrivial nonlinear equations in lower dimensions. This twisted self-duality constraint will be shown to arise in $E_7$ exceptional field theory through a Scherk–Schwarz reduction and we will show how an Eguchi–Hanson gravitational instanton also obeys the twisted self-duality condition.

An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such a perturbative amplitude is related to many important physical process treated in the Standard Model context. The background of this investigation is an alternative strategy to handle the divergences typical for perturbative solutions of quantum field theory. Since its proposition, the mentioned method was exhaustively used to calculate and manipulate one-loop Feynman integrals with a great success. However, the great advances in precision of experimental data collected in particle physics colliders have pushed up theoretical physicists to improve their predictions through multi-loop calculations. In this paper, we describe the main steps required to perform two-loop calculations within the context of the referred method. We show that the same rules used for one-loop calculations are enough to deal with two-loop graphs as well. Analytic results for the sunrise graph are obtained in terms of elliptic multiple polylogarithms as well as a numerical analysis is provided.

This study is devoted to investigate the implementation of machine learning methodologies in the prediction of Quark–anti-Quark bound state spectrum. Predictions are produced by using variety of machine learning (ML) approaches, such as ridge regression, random forest regression, linear regression and K-nearest neighbors regression methods. The forecasts are then evaluated and contrasted in order to determine the optimal performance. Furthermore, systematic comparison of the considered ML methods in terms of percentage of performance is done. Each of the four strategies yielded comparable results. With accuracy of 99%, the ridge regression model exhibited the highest level of predictive performance.

In this paper, we compute the full vacuum polarization tensor in the fermion sector of Lorentz-violating quantum electrodynamics (QED). It turns out to be that even if we assume momentum routing invariance of the Feynman diagrams, it is not possible to fix all surface terms and find an ambiguity-free vacuum polarization tensor. The high- and low-energy limits of this tensor are obtained explicitly. In the high-energy limit, only $c_{\mu \nu }$ coefficients contribute to the result. In the low-energy limit, we find that Lorentz-violating-induced terms depend on $b_{\mu }$, $c_{\mu \nu }$ and $g_{\mu \nu \lambda }$ coefficients and vanish at $p=0$. At small $p$, we succeeded to obtain implications for condensed matter systems, explicitly, for the Hall effect in Weyl semi-metals.