International Journal of Modern Physics A

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired.

After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

A four-dimensional superstring have been constructed starting from a 26-dimensional bosonic string. Fermions are introduced by noting the Mandelstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO(6) ⊗ SO(5) in the worldsheet. It has four bosonic coordinates and 44 Majorana fermions of SO(3, 1). Here the superstring action is shown to be invariant under conformal and superconformal transformations with the usual conformal and superconformal ghosts of the ten-dimensional superstrings. The massless spectrum obtained by quantizing the action, contain vector mesons which are generators of the SO(6) ⊗ SO(5). Using Wilson loops, this product group is proven to descend to Z₃ ⊗ SU(3) ⊗ SU(2) ⊗ U(1) without breaking supersymmetry. Thus there are just three generations of quarks and leptons.

We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean path integral formalism obtained before.

We study a neutron in an external magnetic field in coordinate space and show that the 2 × 2 radial matrix operators that factorize the Hamiltonian are contained within the constants of motion of the problem. Also we show that the 2 × 2 partners Hamiltonians satisfy the shape invariance condition.

The construction of a multidifferential complex, i.e. a differential complex with many differential operators, is presented. By a suitable choice of generators, the differentials become anticommuting and can generate a (co)homological resolution. A concrete construction of a n-differential complex is presented and its application to the BRST description of a gauge theory, with a special look at the Yang–Mills model, is considered.

Topological structure of vortex line in quantum mechanics is studied and classified by Hopf index, linking number in geometry. A mechanism of generation or annihilation of vortex line is given by method of phase singularity theory. The dynamic behavior of vortex line at the critical points is discussed in detail, and three kinds of length approximation relations are given.

Black hole production at the Large Hadron Collider (LHC) was first discussed in 1999. Since then, much work has been performed in predicting the black hole cross-section. In light of the start up of the LHC, it is now timely to review the state of these calculations. We review the uncertainties in estimating the black hole cross-section in higher dimensions. One would like to make this estimate as precise as possible since the predicted values, or lower limits, obtain for the fundamental Planck scale and number of extra dimensions from experiments will depend directly on the accuracy of the cross-section. Based on the current knowledge of the cross-section, we give a range of lower limits on the fundamental Planck scale that could be obtained at LHC energies.

Basing on the general photon eigenstate and the anomaly cancellation, we have naturally explained the electric charge quantization in two models based on the SU(3)_C ⊗ SU(3)_L ⊗ U(1)_X gauge group, namely in the minimal model and in the model with right-handed neutrinos. In addition, we have shown that the electric charges of the proton and of the electron are opposite; and the same happens with the neutron and the neutrino. We argue that the electric charge quantization in these models is closely related with the generation number problem. In fact, both problems are properly solved as the direct consequences of the fermion content under the anomaly free conditions.

It is shown that QCD sum rules in the planar limit lead to a certain relation between four important quantities: ρ-meson mass, weak π-meson decay constant, quark and gluon condensates. As a byproduct an explanation for the dominance of ρρ-decay for the f₀(1370)-meson is proposed.

We give a review and present a comprehensive calculation for the leptonic constant f_Bc of the low-lying pseudoscalar and vector states of B_c-meson in the framework of static and QCD-motivated nonrelativistic potential models taking into account the one-loop and two-loop QCD corrections in the short distance coefficient that governs the leptonic constant of B_c quarkonium system. Further, we use the scaling relation to predict the leptonic constant of the nS-states of the system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.