International Journal of Modern Physics A

We discuss in this paper the usefulness of the effective Lagrangians $({\mathcal{ℒ}}^{\text{eff}})$ of QED and QCD within the one-loop approximation. Instead of calculating ${\mathcal{ℒ}}^{\text{eff}}$ via complicated computations with Schwinger’s proper-time technique or Feynman graphs, we prefer to employ the energy–momentum tensor and the leading-log model. The advantage is that we do not have to demand the external electromagnetic or color field to be constant. There are also some critical remarks added which cast doubt on the use of ${\mathcal{ℒ}}_{\text{QCD}}$ with covariant constant fields in explaining the nature of the QCD vacuum.

The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries.

On the other hand, following Einstein point of view the manifold ${ℳ}$ and the metric should be built simultaneously when solving Einstein’s equation $R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }=T_{\mu \nu }$. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field $(g_{\mu \nu })$ describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on $g_{\mu \nu }$. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. ${}^{34}$ Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies.

Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

In an earlier paper, gauge invariant and background covariant equations for closed string modes were obtained from the exact Renormalization Group of the world sheet theory. The background metric (but not the physical metric) had to be flat and hence the method was not manifestly background independent. In this paper, the restrictions on the background metric are relaxed. A simple prescription for the map from loop variables to space–time fields is given whereby for arbitrary backgrounds the equations are generally covariant and gauge invariant. Extra terms involving couplings of the curvature tensor to (derivatives of) the Stueckelberg fields have to be added. The background metric can thus be chosen to be the physical metric without any restrictions. This method thus gives manifestly background independent equations of motion for both open and closed string modes.

The masses and decay constants of the light tensor mesons were calculated with quantum numbers $J^P=2^{+}$ in the framework of the QCD sum rules in the standard model. The non perturbative contributions up to dimension-5 are considered as important terms of the operator product expansion.

We propose a framework for a new type of finite field theories based on a hidden duality between an ultraviolet and an infrared region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of the duality transformation, and this feature is compatible with models possessing a specific fermionic symmetry. Theories can be tested indirectly by relations among parameters, reflecting underlying symmetries.

We investigate and classify the possible types of false vacuum bubbles in Einstein gravity. The false vacuum bubbles can occur only if gravity is taken into account. We show that there exist solutions only with compact geometries. The analytic computations for the radius and nucleation rate of a vacuum bubble are evaluated using the thin-wall approximation. We discuss possible cosmological implications of our new solutions.

We present predictions for the inclusive production of charm jets in proton–proton collisions at 7 TeV. Several CTEQ parton distribution functions (PDFs) of the CTEQ6.6M type are employed, where two of the CTEQ6.6 PDFs have intrinsic charm. At large enough jet transverse momentum and large jet rapidity, the intrinsic charm content can be tested.

Using a superfield generalization of the tadpole method, we study the one-loop effective potential for a Wess–Zumino model modified by a higher derivative term, inspired by the Lee–Wick model. The one-loop Kählerian potential is also obtained by other methods and compared with the effective potential.

We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}2{\pi }^0$ process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the ${\gamma }^{\ast }\to 4\pi$ vertex using a vector meson dominance model, including the intermediate resonance contributions relevant at these energies. We find that ${\mu }_{\rho }=2.1\pm 0.5$ in $e∕2m_{\rho }$ units.

We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory.

We investigate some aspects of the thermal history of the early universe according to Yang–Mills Gravity (YMG); a gauge theory of gravity set in flat space–time. Specifically, equations for the ionization fractions of hydrogen and singly ionized helium during the recombination epoch are deduced analytically and then solved numerically. By considering several approximations, we find that the presence of primordial helium and its interaction with Lyman series photons has a much stronger effect on the overall free electron density in YMG than it does in the standard, General Relativity (GR)-based, model. Compared to the standard model, recombination happens over a much larger range of temperatures, although there is still a very sharp temperature of last scattering around 2000 K. The ionization history of the universe is not directly observable, but knowledge of it is necessary for CMB power spectrum calculations. Such calculations will provide another rigorous test of YMG and will be explored in detail in an upcoming paper.