International Journal of Modern Physics A

We study the conditions for the existence of black holes that can be produced in colliders at the TeV-scale if the space–time is higher dimensional. On employing the microcanonical picture, we find that their life-times strongly depend on the details of the model. If the extra dimensions are compact (ADD model), microcanonical deviations from thermality are in general significant near the fundamental TeV mass, and tiny black holes decay more slowly than predicted by the canonical expression but still fast enough to disappear almost instantaneously. However, with one warped extra dimension (RS model), microcanonical corrections are much larger and tiny black holes appear to be (meta)stable. Further, if the total charge is not zero, we argue that naked singularities do not occur provided the electromagnetic field is strictly confined on an infinitely thin brane. However, they might be produced in colliders if the effective thickness of the brane is of the order of the fundamental length scale (~TeV^-1).

We present a class of static membrane solutions, with nonflat world volume geometry, in the eleven-dimensional supergravity with source terms. This class of solutions contains supersymmetric as well as a large class of nonsupersymmetric configurations. We comment about the near horizon limit and stability of these solutions and point out an interesting relation with a certain two-dimensional dilaton gravity system.

Certain quasi-exactly solvable systems exhibit an energy reflection property that relates the energy levels of a potential or of a pair of potentials. We investigate two sister potentials and show the existence of this energy reflection relationship between the two potentials. We establish a relationship between the lowest energy edge in the first potential using the weak coupling expansion and the highest energy level in the sister potential using a WKB approximation carried out to higher order.

It is argued that the newly introduced moments of rapidity gaps for the event-by-event fluctuations depends on the number of events and multiplicity. The interesting ones are unstable under ISR energies of h–h collisions. The instability is well improved when multiplicity increases.

We show that many topological and geometrical properties of complex projective space can be understood just by looking at a suitably constructed picture. The idea is to view CPⁿ as a set of flat tori parametrized by the positive octant of a round sphere. We pay particular attention to submanifolds of constant entanglement in CP³ and give a few new results concerning them.

Low energy theorems of Nambu–Goldstone fermion associated with spontaneously broken supersymmetry are studied for gauge supermultiplets. Two possible terms in the effective Lagrangian are needed to deal with massless gaugino and/or massless gauge boson. As an illustrative example, a concrete model is worked out which can interpolate massless as well as massive gaugino and/or gauge boson to examine the low energy effective interaction of NG-fermion.

Measuring the photon energy spectrum in radiative B decays provides essential help for gaining theoretical control over semileptonic B transitions. The hadronic recoil mass distribution in B → X_u ℓ ν promises the best environment for determining |V_ub|. The theoretical uncertainties are largest in the domain of low values of the lepton pair mass q². Universality relations allow us to describe this domain reliably in terms of the photon spectrum in B → X_s + γ. A method is proposed to incorporate 1/m_b corrections into this relation. The low-E_γ tail in radiative decays is important in the context of extracting |V_ub|. We argue that CLEO's recent fit to the spectrum underestimates the fraction of the photon spectrum below 27thinsp;GeV. Potentially significant uncertainties enter in the theoretical evaluation of the integrated end point lepton spectrum or the B → X_u ℓ ν width with a too high value of the lower cut on q² in alternative approaches to |V_ub|.

We study Myers' world volume effective action of coincident D-branes. We investigate a system of N₀D0-branes in the geometry of Dp-branes with p = 2 or p = 4. The choice of coordinates can make the action simplified and tractable. For p = 4, we show that a certain pointlike D0-brane configuration solving equations of motion of the action can expand to form a fuzzy two-sphere via magnetic moment effect without changing quantum numbers. We compare noncommutative D0-brane configurations with dual spherical D(6 - p)-brane systems. We also discuss the relation between these configurations and giant gravitons in 11 dimensions.

We consider a ϕ⁴ model in 1+1 dimensions modified by the addition of an extra kinetic term similar to the Skyrme term in higher dimensions and a potential term. We generalize the procedures of the leading order method to include elliptic functions and obtain cnoidal wave type solutions of the familiar ϕ⁴ model. As a limit case, we re-obtain the well-known solitary and travelling wave solutions of this model from the constructed cnoidal wave solutions. A further kink solution of the pure ϕ⁴ model is also obtained. We obtain soliton solutions of the modified ϕ⁴ model and show that it possesses two ϕ⁴ kink solutions, with the same velocity and total energy, as well as a double-kink solution. We study some properties of the modified model. In particular, we see that the two ϕ⁴ kinks have a definite velocity and this velocity is a critical velocity for the double-kink structures. Finally, we conclude the paper with some features and comments.

Following the work of David Fairlie and his collaborators, we discuss the geometry of the equations of motion for the companion Lagrangian. This arises while we attempt to construct the field theoretic Lagrangians for strings and branes. These equations are related to generalized Bateman equations. Interestingly, an inhomogeneous form of these equations are related to what Dubrovin and Novikov called equations of the hydrodynamic type. We translate this set of equations into (Nambu)–Poisson equations and formulate the Lax representation of these systems. We deform all this set of equations by the Moyal product. We also present the Lax pair of the Moyal deformed systems for some special cases.

In this paper, we investigate the Jordanian analog of Yang–Mills theory. For h = 0, this is just the usual one as it should be. We compute the h-trace which leads to the h-metric. This Jordanian quantum metric is an important ingredient for the construction of a U_h(2) Yang–Mills Lagrangian. Finally, we find the Weinberg angle in terms of this h-metric.

One-dimensional Klein–Gordon equation with screened Coulomb potential generates genuine bound states in the scalar coupling scheme. In this article we have obtained the exact solutions of the problem. The results are compared with those of the vector coupling scheme.

In a recent work⁷ we showed that for a Hamiltonian system with constraints, the set of constraints can be investigated in the first- and second-class constraint chains. We show here that using this "chain-by-chain" method for an arbitrary system. One can fix the gauges in the most economical and consistent way. We show that it is enough to assume some gauge fixing conditions conjugate to the last elements of first-class chains. The remaining necessary conditions would emerge from consistency conditions.