On zero modes of the eleven dimensional superstring

It is shown that recently pointed out by Berkovits on-shell degrees of freedom of the D=11 superstring do not make contributions into the quantum states spectrum of the theory. As a consequence, the spectrum coincides with that of the D=10 type IIA superstring.Comment: 7 pages, LaTex fil

On possible generalization of the superstring action to eleven dimensions

We suggest a D=11 super Poincar\'e invariant action for the superstring which has free dynamics in the physical variables sector. Instead of the standard approach based on the searching for an action with local $\kappa$-symmetry (or, equivalently, with corresponding first class constraints), we propose a theory with fermionic constraints of second class only. Then the $\kappa$-symmetry and the well known $\Gamma$-matrix identities are not necessary for the construction. Thus, at the classical level, the superstring action of the type described can exist in any spacetime dimensions and the known brane-scan can be revisited.Comment: 23 pages, RevTex file, to be published in Phys. Rev.

Spherical Pendulum Small Oscillations for Slewing Crane Motion

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies’ problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown

On minimal coupling of the ABC-superparticle to supergravity background

By rigorous application of the Hamiltonian methods we show that the ABC-formulation of the Siegel superparticle admits consistent minimal coupling to external supergravity. The consistency check proves to involve all the supergravity constraints.Comment: 8 pages RevTex file, to appear in Phys. Rev.

Generalized action principle and extrinsic geometry for N=1 superparticle

It is proposed the generalized action functional for N=1 superparticle in D=3,4,6 and 10 space-time dimensions. The superfield geometric approach equations describing superparticle motion in terms of extrinsic geometry of the worldline superspace are obtained on the base of the generalized action. The off-shell superdiffeomorphism invariance (in the rheonomic sense) of the superparticle generalized action is proved. It was demonstrated that the half of the fermionic and one bosonic (super)fields disappear from the generalized action in the analytical basis. Superparticle interaction with Abelian gauge theory is considered in the framework of this formulation. The geometric approach equations describing superparticle motion in Abelian background are obtained.Comment: 31 pages. Late

Lagrangian approach to the physical degree of freedom count

In this paper, we present a Lagrangian method that allows the physical degree of freedom count for any Lagrangian system without having to perform neither Dirac nor covariant canonical analyses. The essence of our method is to establish a map between the relevant Lagrangian parameters of the current approach and the Hamiltonian parameters that enter in the formula for the counting of the physical degrees of freedom as is given in Dirac’s method. Once the map is obtained, the usual Hamiltonian formula for the counting can be expressed in terms of Lagrangian parameters only, and therefore we can remain in the Lagrangian side without having to go to the Hamiltonian one. Using the map, it is also possible to count the number of first and second-class constraints within the Lagrangian formalism only. For the sake of completeness, the geometric structure underlying the current approach—developed for systems with a finite number of degrees of freedom—is uncovered with the help of the covariant canonical formalism. Finally, the method is illustrated in several examples, including the relativistic free particle.Warm thanks to J. D. Vergara for his valuable comments on the subject of this paper. This work was supported in part by CONACyT, México, Grant Nos. 167477-F and 132061-F

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.Comment: New references added, Published online in Foundations of Physic

3 DOF Spherical Pendulum Oscillations with a Uniform Slewing Pivot Center and a Small Angle Assumption

The present paper addresses the derivation of a 3 DOF mathematical model of a spherical pendulum attached to a crane boom tip for uniform slewing motion of the crane. The governing nonlinear DAE-based system for crane boom uniform slewing has been proposed, numerically solved, and experimentally verified. The proposed nonlinear and linearized models have been derived with an introduction of Cartesian coordinates. The linearized model with small angle assumption has an analytical solution. The relative and absolute payload trajectories have been derived. The amplitudes of load oscillations, which depend on computed initial conditions, have been estimated. The dependence of natural frequencies on the transport inertia forces and gravity forces has been computed. The conservative system, which contains first time derivatives of coordinates without oscillation damping, has been derived. The dynamic analogy between crane boom-driven payload swaying motion and Foucault’s pendulum motion has been grounded and outlined. For a small swaying angle, good agreement between theoretical and averaged experimental results was obtained