International Journal of Modern Physics A

String/M-theory is an exciting framework within which we try to understand our universe and its properties. Compactified string/M-theories address and offer solutions to almost every important question and issue in particle physics and particle cosmology. But earlier goals of finding a top–down “vacuum selection” principle and deriving the 4D theory have not yet been realized. Does that mean we should stop trying, as nearly all string theorists have? Or can we proceed in the historical way to make a few generic, robust assumptions not closely related to observables, and follow where they lead to testable predictions and explanations? Making only very generic assumptions is a significant issue. I discuss how to try to proceed with this approach, particularly in M-theory compactified on a 7D manifold of G₂ holonomy. One goal is to understand our universe as a string/M-theory vacuum for its own sake, in the long tradition of trying to understand our world, and what that implies. In addition, understanding our vacuum may be a prelude to understanding its connection to the multiverse.

We review the present situation in top quark physics, in these early days of Run II of the LHC. We take mostly a Standard Model perspective, showing recent results, and review the key concepts and results of the associated theoretical predictions. The issues we discuss are the top quark mass, top quark pair and single top production, production in association with other particles, charge asymmetry and top quark decay.

This paper is an exposition of the relationship between Witten’s Chern–Simons functional integral and the theory of Vassiliev invariants of knots and links in three-dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory. This approach makes it possible to discuss the mathematics intrinsic to the functional integral rigorously and without functional integration. Applications to loop quantum gravity are discussed.

We calculate the uncertainties in the position and momentum of a particle in the 1D potential $V(x)=F\left|x\right|$, $F>0$, when the position and momentum operators obey the deformed commutation relation $[\widehat{x},\widehat{p}]=i\hslash (1+\beta {\widehat{p}}^2)$, $\beta >0$. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian ${Ĥ}_1={\widehat{p}}^2/2m+F\left|\widehat{x}\right|$ admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as $\mathrm{\Delta }x\sim 1/\mathrm{\Delta }p$ as in the $\beta =0$ limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had $\mathrm{\Delta }x\sim \mathrm{\Delta }p$, both $\mathrm{\Delta }x$ and $\mathrm{\Delta }p$ diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.

We study particle creation in a single pulse of an electric field in scalar quantum electrodynamics. We investigate the parameter condition for the case where the dynamical pair creation and Schwinger mechanism respectively dominate. Then, an asymptotic expansion for the particle distribution in terms of the time interval of the applied electric field is derived. We compare our result with particle creation in a constant electric field with a finite-time interval. These results coincide in an extremely strong field, however they differ in general field strength. We interpret the reason of this difference as a nonperturbative effect of high-frequency photons in external electric fields. Moreover, we find that the next-to-leading-order term in our asymptotic expansion coincides with the derivative expansion of the effective action.

By attaching three anticommuting Lorentz scalar (color) property coordinates to space–time, with an appropriate extended metric, we unify gravity with chromodynamics: gauge transformations then just correspond to coordinate transformations in the enlarged space–time-property space.

The paper aims to consider the electromagnetic adjoint-field in the complex octonion space as the dark matter field, describing some properties of the dark matter, especially the origin, particle category, existence region, force and so forth. Since Maxwell applied the algebra of quaternions to depict the electromagnetic theory, some scholars adopt the complex quaternion and octonion to study the physics property of electromagnetic and gravitational fields. In the paper, by means of the octonion operator, it is found that the gravitational field accompanies with one adjoint-field, whose property is partly similar to that of electromagnetic field. The electromagnetic field accompanies with another adjoint-field, whose feature is partly similar to that of gravitational field. As a result, the electromagnetic adjoint-field can be chosen as one candidate of the dark matter field. According to the electromagnetic adjoint-field, it is able to predict a few properties of the dark matter, for instance, the particle category, interaction intensity, interaction distance, existence region and so forth. The study reveals that the dark matter particle and the gravitational resource will be influenced by the gravitational strength and force. The dark matter field is capable of making a contribution to physics quantities of gravitational field, including the angular momentum, torque, energy, force and so on. Further, there may be comparatively more chances to discover the dark matter in some regions with the ultrastrong field strength, surrounding the neutral star, white dwarf, galactic nucleus, black hole, astrophysical jet and so on.

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an external harmonic potential.

We study the changes of the mass and width of the sigma meson in the framework of the Linear Sigma Model at finite temperature, in the one-loop approximation. We have found that as the temperature increases, the mass of sigma shifts down. We have also analyzed the $\sigma$-spectral function and we observe an enhancement at the threshold which is a signature of partial restoration of chiral symmetry, also interpreted as a tendency to chiral phase transition. Additionally, we studied the width of the sigma, when the threshold enhancement takes place, for different values of the sigma mass. We found that there is a brief enlargement followed by an abrupt fall in the width as the temperature increases, which is also related with the restoration of chiral symmetry and an indication that the sigma is a bound state of two pions.

The $Z\to \gamma \gamma$ and $Z\to gg$ decays are studied in the context of the renormalizable version of the Standard Model Extension. The $CPT$-odd $\bar{\psi }{\gamma }_5/b\psi$ bilinear interaction, which involves the constant background field $b_{\alpha }$ and which has been a subject of interest in literature, is considered. It is shown that the $Z\to \gamma \gamma$ and $Z\to gg$ decays, which are strictly zero in the standard model, can be generated radiatively at the one-loop level. It is found that these decays are gauge invariant and free of ultraviolet divergences, and that the corresponding decay widths only depend on the spatial component of the background field $b$.