Massive "spin-2" theories in arbitrary D≥3D \ge 3 dimensions

Here we show that in arbitrary dimensions $D\ge 3$ there are two families of second order Lagrangians describing massive "spin-2" particles via a nonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory in general. At zero mass one of the families is Weyl invariant. Such massless theory has no particle content in $D=3$ and gives rise, via master action, to a dual higher order (in derivatives) description of massive spin-2 particles in $D=3$ where both the second and the fourth order terms are Weyl invariant, contrary to the linearized New Massive Gravity. However, only the fourth order term is invariant under arbitrary antisymmetric shifts. Consequently, the antisymmetric part of the tensor $e_{[\mu\nu]}$ propagates at large momentum as $1/p^2$ instead of $1/p^4$. So, the same kind of obstacle for the renormalizability of the New Massive Gravity reappears in this nonsymmetric higher order description of massive spin-2 particles.Comment: 11 pages, 0 figure

Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion

Here we obtain alternative descriptions of massive spin-2 particles by an embedding procedure of the Fierz-Pauli equations of motion. All models are free of ghosts at quadratic level although most of them are of higher order in derivatives. The models that we obtain can be nonlinearly completed in terms of a dynamic and a fixed metric. They include some $f(R)$ massive gravities recently considered in the literature. In some cases there is an infrared (no derivative) modification of the Fierz-Pauli mass term altogether with higher order terms in derivatives. The analytic structure of the propagator of the corresponding free theories is not affected by the extra terms in the action as compared to the usual second order Fierz-Pauli theory.Comment: 13 page

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques.Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Classical Rotons in Cold Atomic Traps

We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-topical traps, multiple-scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the re-scattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces results on a new polariton mode, which exhibits a roton minimum. Making use of Feynman's formula for the static structure factor, we show that the roton minimum is related to the appearance of long-range order in the system.Comment: 5 pages, 3 figure