The aim of the paper is to prove that T M , the tangent space of order k ≥ 1 of a manifold M , is diffeomorphic with T 1 k M , the tangent space of k–velocities, and also with ( T 1 k )∗ M , the cotangent space of k–covelocities, via suitable Lagrangians. One prove also that a hyperregular Lagrangian of first order on M can give rise to such diffeomorphisms. M.S.C. 2000: 53C60, 53C80, 70H50.

In a system consisting of a single particle in a potential, the classical action *L dt is the number of phase waves that pass through the moving particle, as the particle moves from its initial to its final position. Thus the Lagrangian can be cast into the form L5p(vg2vp), where vg and vp are the group and phase velocities and p is the momentum. © 2003 American Association of Physics Teachers....

We characterize non-degenerate Lagrangians of the form

We derive the simplest form of the κ(κ) order graviton self-interaction Lagrangian density Lg(Lg) in the weak field approximation. With the divergenceless condition, de Donder gauge and some combinatoric techniques, we derive the mathematically independent basis expressions for Lg(Lg) composed of 8(24) terms. By using the basis expressions Lg(Lg) is reduced to 6(18) terms. [email protected]...

We determine all tight Lagrangian surfaces in S 2 × S 2. In particular, globally tight Lagrangian surfaces in S 2 × S 2 are nothing but real forms.

The interaction of dyons in the mean field approximation is considered. The result of interaction is the mass term for dyonic field in the effective Lagrangian. Due to the mass term the profile function of dyon falls off exponentially at large distances.

Much research has been done in the latter years on the subject of Lorentz violation induced by Quantum Gravity effects. On the theoretical side it has been shown that both Loop Quantum Gravity and String Theory predict that Lorentz violation can be induced at an energy near to the Planck scale. On the other hand, most of the experimental results in the latter years, have confirmed that the laws...

The top-quark system as a probe for new physics is considered using a consistent, gauge-invariant effective Lagrangian approach. The magnitude of new effects is estimated and the results are applied to top production through W fusion. Other processes are also briefly discussed.