On the Nonrelativistic Limit of the phi^4 Theory in 2+1 Dimensions

We study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self-interaction. The two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states. From this result and the two loop computation of the self energy correction, we determine an effective nonrelativistic action.Comment: 15 pages, 2 figures, revte

Flag-Dipole Spinor Fields in ESK Gravities

We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on $f(R)$ and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given for instance by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle.Comment: 18 pages, improved versio

Five-Dimensional f(R) Braneworld Models

After incorporating the f(R) gravity into the general braneworld sum rules scope, it is shown that some particular class of warped five dimensional nonlinear braneworld models, which may be interesting for the hierarchy problem solution, still require a negative tension brane. For other classes of warp factors (suitable and not suitable for approaching the hierarchy problem) it is not necessary any negative brane tension in the compactification scheme. In this vein, it is argued that in the bulk f(R) gravity context, some types of warp factors may be useful for approaching the hierarchy problem and for evading the necessity of a negative brane tension in the compactification scheme.Comment: 10 pages, references updated, small modifications. Accepted for publication in Phys. Rev.

Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spacial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external e.m. field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, $\Delta x\Delta y\geq\theta^{2}/2$, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.Comment: 11 pages, references adda