We show that the minimization of the Lagrangian action functional on suitable classes of symmetric loops yields collisionless periodic orbits of the n-body problem, provided that some simple conditions on the symmetry group are satisfied. More precisely, we give a fairly general condition on symmetry groups G of the loop space Λ for the n-body problem (with potential of homogeneous degree −α, w...

Novel Lagrangians are discussed in which (non-abelian) electric and magnetic gauge fields appear on a par. To ensure that these Lagrangians describe the correct number of degrees of freedom, tensor gauge fields are included with corresponding gauge symmetries. Non-abelian gauge symmetries that involve both the electric and the magnetic gauge fields can then be realized at the level of a single ...

Modern spectroscopic data on light non-strange meson spectrum is analyzed. It is argued that the observed regularities of experimental spectrum for highly excited states favour a partial restoration of all approximate classical symmetries of QCD Lagrangian (conformal, chiral and axial) broken by the quantum corrections. The rate of restoration of classical symmetries is estimated. The dependenc...

We argue that the non-observability of the spontaneous breakdown of Lorentz symmetry (SBLS) caused by the vacuum expectation values of vector fields could provide the origin of all internal symmetries observed. Remarkably , the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the app...

Compact Type IIB D = 4, N = 1 orientifolds have certain U(1) σ-model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of ZN orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singulari...

We develop several formal analogies between the logistic equation and spatially homogeneous isotropic relativistic cosmology described by Einstein–Friedmann equations. These produce an effective Lagrangian Hamiltonian new symmetries for equation.

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagra...