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

Multiperiodic magnetic structures in Hubbard superlattices

We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive (i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG) diagonalization of finite systems is used to calculate the local moment and the magnetic structure factor in the ground state. We have found four regimes for magnetic behavior: uniform local moments forming a spin-density wave (SDW), `floppy' local moments with short-ranged correlations, local moments on repulsive sites forming long-period SDW's superimposed with short-ranged correlations, and local moments on repulsive sites solely with long-period SDW's; the boundaries between these regimes depend on the range of electronic densities, rho, and on the SL aspect ratio. Above a critical electronic density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and with the spacer thickness. The former oscillation allows one to reproduce all SDW wave vectors within a small range of electronic densities, unlike the homogeneous system. The latter oscillation is related to the exchange oscillation observed in magnetic multilayers. A crossover between regimes of `thin' to `thick' layers has also been observed.Comment: 9 two-column pages, 10 figure

Coherent State Path Integrals in the Weyl Representation

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}, which involve the normal or the antinormal ordering of the Hamiltonian. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. We show that the semiclassical limit of the coherent state propagator in Weyl representation is involves classical trajectories that are independent on the coherent states width. This propagator is also free from the phase corrections found in \cite{Bar01} for the two Klauder forms and provides an explicit connection between the Wigner and the Husimi representations of the evolution operator.Comment: 23 page