International Journal of Modern Physics A

The role of the bound electron Green function in the recent high precision determination of the electron mass is discussed. Emphasis is placed on the connection to Schwinger’s use of such Green functions in his early work establishing the modern form of QED, his calculation of leading binding corrections, and his work on synchrotron radiation.

We explore a model akin to axion electrodynamics in which the axion field $𝜃(t,x)$ rather than being dynamical is a piecewise constant effective parameter $𝜃$ encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a $𝜃$-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green’s function formulation of what amounts to typical boundary-value problems of $𝜃$-media, when external sources or boundary conditions are given. As an illustration of our methods, which we have also extended to ponderable media, we interpret the constant $𝜃$ as a novel topological property of vacuum, a so called $𝜃$-vacuum, and restrict our discussion to the cases where the permittivity and the permeability of the media is one. In this way we concentrate upon the effects of the additional $𝜃$ coupling which induce remarkable magnetoelectric effects. The issue of boundary conditions for electromagnetic radiation is crucial for the occurrence of the Casimir effect, therefore we apply the methods described above as an alternative way to approach the modifications to the Casimir effect by the inclusion of topological insulators.

The classic electromagnetic energy–momentum problem in matter (usually called the Abraham–Minkowski problem) has attracted increased interest, as is natural in relation to the several impressive radiation pressure experiments that have appeared recently. Our intention with the present note is to focus attention on some of these results, and also to give a warning against premature interpretations of the observations. One sees often in the literature that the observable deflections of dielectric surfaces are interpreted so as to mean that the so-called Abraham term is a chief ingredient. Usually this is not so, however. Most of the experimental results are actually explainable by the surface forces at the dielectric surfaces, eventually augmented by Lorentz forces in the interior, and do not involve the Abraham momentum as such. For concreteness we focus mainly on a simplified version of the experiment of Kundu et al. (2017), but extend the analysis somewhat by including time-dependent resonance phenomena. In a short appendix we discuss also the connection with the Casimir effect.

We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

When ground-state atoms are accelerated and the field with which they interact is in its normal vacuum state, the atoms detect Unruh radiation. We show that atoms falling into a black hole emit acceleration radiation which, under appropriate initial conditions (Boulware vacuum), has an energy spectrum which looks much like Hawking radiation. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. The Unruh temperature can also be obtained by using the Kubo–Martin–Schwinger (KMS) periodicity of the two-point thermal correlation function, for a system undergoing uniform acceleration; as with much of the material in this paper, this known result is obtained with a twist.

This paper investigates the cosmological dynamics of the Hessence scalar field coupled with the dark matter in the background of the teleparallel gravity. We have assumed that the potential of the scalar field is exponential in nature whereas the $f(T)$ appearing in the teleparallel theory has the form $f(T)=\beta {(-T)}^{\frac{1}{2}}$. The field equations of this system reduce to a nonlinear autonomous system and dynamical system analysis is then performed. Due to the nonlinearity and the existence of multiple zero eigenvalues, the traditional procedures of analysis break down. So some novel technique is required. One of the latest such techniques is the invariant manifold theory. By the application of this theory, one projects the variables linked with the zero eigenvalues onto the variables linked with the nonzero eigenvalues to compute the center manifolds and the reduced systems associated with the critical points. These reduced systems reflect the nature of the whole dynamical systems. They also have less dimension and are often simple in nature. Hence, it is possible to solve them directly. In this paper, we work exactly in this spirit and find the center manifolds and solve the corresponding reduced system for some of the critical points associated with the dynamical system. We discover some interesting results namely that there are certain bounds on the interaction term $\delta$ which asserts the stability of the systems. We also present various stability diagrams of the reduced systems. An asymptotic analysis is then done for the critical points at infinity. Finally, we discuss the cosmological interpretation of our results.

In this paper, we consider higher-order correction of the entropy and study the thermodynamical properties of recently proposed Schwarzschild–Beltrami–de Sitter black hole, which is indeed an exact solution of Einstein equation with a positive cosmological constant. By using the corrected entropy and Hawking temperature, we extract some thermodynamical quantities like Gibbs and Helmholtz free energies and heat capacity. We also investigate the first and second laws of thermodynamics. We find that presence of higher-order corrections, which come from thermal fluctuations, may remove some instabilities of the black hole. Also unstable to stable phase transition is possible in presence of the first- and second-order corrections.

The generation of neutrino beams at proton accelerators is a difficult scientific and engineering problem. To obtain narrow directional neutrino beams for experiments, intense extracted proton beams are used, secondary particles ($\pi$ and $K$ mesons) are generated at an external target. Further, to obtain parallel beams of these neutrino parent particles, high-current electromagnetic lenses are used. In this work, a surprisingly simple method based on a crystal focusing device has been proposed to obtain neutrino beams. Neutrino fluxes are calculated in comparison with the traditional scheme.

A number of derivations of the standard neutrino oscillation formula are known, each one providing its own unique insights. Common to all treatments is the assumption that neutrinos propagate freely between source and detector, as indeed they do in all experiments thus far conducted. Here, we consider how neutrinos oscillate when contrary to the usual setup, they are bound in a potential well. The focus in particular is on nonrelativistic neutrinos with quasi-degenerate masses, for which oscillations in free space are described by the same formula, to lowest order, as relativistic neutrinos. Trapping these particles engenders corrections to their oscillation frequencies because the interference terms are between discrete energy levels rather than continuous spectra. Especially novel is the frequency shift that occurs due to the dependence of the energy levels on the mass of the neutrino: this part of the correction is nonvanishing even in the extremely nonrelativistic limit, reflecting the fact that the neutrino mass states have different zero-point energies in the well. Building an apparatus that can trap neutrinos is a futuristic prospect to say the least, but these calculations nonetheless shine a light on certain basic aspects of the flavor-oscillation phenomenon.

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, ${\tau }^{-}\to {\pi }^{-}\gamma {\nu }_{\tau }$, have been investigated. We present the analytical results for the $t$-distribution of the partial differential widths, which are responsible for different polarization phenomena, in the case of the photon energy cut: $\omega >X$. These quantities depend on the invariant mass squared $t$ of the pseudoscalar meson and photon and the photon energy cut $X.$ Our analytical formulae, in terms of the weak vector and axial-vector form factors, describing the structure-dependent part of the decay amplitude, are valid also for the decay ${\tau }^{\pm }\to K^{\pm }{\nu }_{\tau }\gamma$ after trivial substitutions of the corresponding constants. We demonstrate the essential decrease of the inner bremsstrahlung contribution in comparison with the structural one with increase of the photon cut energy. In numerical calculations, the vector and axial-vector form factors are determined using the chiral effective theory with resonances (R$\chi$T).

It is said that there are no accidents or coincidences in physics. Within the minimal standard model combined with general relativity, we point out that there are three exceptionally long lifetimes which are consistent with being equal, and hence that there are two unexplained coincidences.

We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

In this paper, we investigate the $q$-deformed Dirac equation. We obtain a quasi-exactly solvable equation. The energy–momentum distribution is considered using Landau–Lifshitz, Einstein and Papapetrou complexes and the results are discussed.

We discuss the extraction of the ground state $〈\mathrm{\text{K}}(p)|V_{\mu }(0)|{\mathrm{\text{B}}}_{\mathrm{\text{s}}}(0)〉$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O$(a)$-improved CLS 2-flavor simulations and the final state momentum is $\left|p\right|=0.5$ GeV. The b-quark is treated in HQET including the $1/m_{\mathrm{\text{b}}}$ corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the $1/m_{\mathrm{\text{b}}}$ corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

In this paper, we assume $X(5568)$ exist and study mass spectrum of $X(5568)$ resonance and its hypothetical charmed partner, $X_c$, by artificial neural network method. The obtained predictions are compared with the experimental data and results of other theoretical works.

Using modular bootstrap we show the lightest primary fields of a unitary compact two-dimensional conformal field theory (with $c$, $\bar{c}>1$) has a conformal weight $h_1\le \frac{c}{12}+{𝒪}(1)$. This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio $\frac{j}{\mathrm{\Delta }}\approx 1$, the corresponding dimension is $\mathrm{\Delta }\le \frac{c}{12}+{𝒪}(1)$. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three-dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three-dimensional gravity has extremal or near extremal BTZ black hole.