Modern Physics Letters A

In this note, I recollect a two-week period in September 1968 when I factorized the Veneziano model using string variables in Chicago. Professor Yoichiro Nambu went on to calculate the N-particle dual resonance model and then to factorize it on an exponential degeneracy of states. That was in 1968 and the following year 1969 he discovered the string action. I also include some other reminiscences of Nambu who passed away on July 5, 2015.

We use comparison with recent LHCb data on single $Z/{\gamma }^{\ast }$ production and decay to lepton pairs as a vehicle to study the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to precision quantum chromodynamics (QCD) calculations, by realistic MC event generator methods, as needed for precision large hadron collider (LHC) physics. This represents an extension of the phase space of our previous studies based on comparison with CMS and ATLAS data, as the pseudo-rapidity range measured by the LHCb for leptons in the data we study is 2.0 $<\eta <$ 4.5 to be compared with $\left|\eta \right|<$ 4.6(2.4) in our previous CMS(ATLAS) data comparison for the same processes. To be precise, for ${\mu }^{+}{\mu }^{-}$ decays, the CMS data had $\left|\eta \right|<$ 2.1 while, for $e^{+}{e}^{-}$ decays, the CMS data had $\left|\eta \right|<$ 2.1 for both leptons for the $Z{\gamma }^{\ast }$$p_T$ spectrum and had one lepton with $\left|\eta \right|<$ 2.5 and one with $\left|\eta \right|<$ 4.6 for the $Z/{\gamma }^{\ast }$ rapidity spectrum. The analyses we present here with the LHCb data thus represent an important addition to our previous results, as it is essential that theoretical predictions be able to control all of the measured phase space at LHC. The level of agreement between the new theory and the data continues to be a reason for optimism.

Using vertex operators acting on fermionic Fock space we prove certain identities, which depend on a number of parameters, generalizing and refining the Nekrasov–Okounkov identity. These identities provide exact product representation for the instanton partition function of certain five-dimensional quiver gauge theories. This product representation also clearly displays the modular transformation properties of the gauge theory partition function.

Recently, it was argued that gravity with the square of the Ricci tensor can be stabilized by adding constraints to the theory in a Lorentz violating way. This was so far demonstrated for fluctuations on the Minkowski/de Sitter background. We show that the same scheme works equally well for removing Ostrogradski’s ghost from fluctuations on a cosmological background in generic $f(R,R_{\mu \nu }^2,C_{\mu \nu \rho \sigma }^2)$-type theories of gravity. As an application, we derive the general formula for the spectrum of primordial tensor perturbations from the stabilized theory. The evolution of matter density perturbations is also discussed.

We study the Einstein equations in the static cylindrically symmetric case with the stress–energy tensor of the form $T_{\nu }^{\mu }=\mathrm{\text{diag}}\{\mu ,-\alpha \mu ,-\beta \mu ,-\gamma \mu \}$, where $\mu$ is an unknown function and $\alpha$, $\beta$, $\gamma$ are arbitrary real constants ($\alpha$ is assumed to be nonzero). The stress–energy tensor of this form includes as special cases several well-known solutions, such as the perfect fluid solution with the barotropic equation of state, the solution with the static electric field and the solution with the massless scalar field. We solve the Einstein equations with this stress–energy tensor and study some properties of the obtained metric.

In this paper, we investigate the electron Landau level stability and its influence on the electron Fermi energy, $E_{\mathrm{\text{F}}}(e)$, in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity $g_n$, the electron Landau level stability coefficient is introduced. According to the requirement that $g_n$ decreases with increasing the magnetic field intensity $B$, the magnetic field index $\beta$ in the expression of $E_{\mathrm{\text{F}}}(e)$ must be positive. By introducing the Dirac-$\delta$ function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to $E_{\mathrm{\text{F}}}(e)$ in a superhigh magnetic field (SMF). This solution has a low magnetic field index of $\beta =1/6$, compared with the previous one, and works when $\rho \ge 10^7{\mathrm{\text{g cm}}}^{-3}$ and $B_{\mathrm{\text{cr}}}\ll B\le 10^{17}$ Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density $n_e$, and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As $B$ increases, more and more electrons will occupy higher Landau levels, though $g_n$ decreases with the Landau level number $n$. The enhanced $n_e$ in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for magnetars.

We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein–Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov–Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov–Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.