We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale, a physical cutoff rendering the quantum field theory finite, can be made compatible with a suppression of Lorentz invariance violations at low momenta. The fine tuning required to get this suppression and to have a light scalar particle in the spectrum is determined at one loop.

We consider a new set of effects arising from the quantum gravity corrections to the propagation of fields, associated with fluctuations of the spacetime geometry. Using already existing experimental data, we can put bounds on these effects that are more stringent by several orders of magnitude than those expected to be obtained in astrophysical observations. In fact, these results can already be interpreted as questioning the whole scenario of linear (in l(P)) corrections to the dispersion relations for free fields in Lorentz violating theories.

Within an early Universe scenario, nonextensive thermostatistics (NET) is investigated on the basis of data concerning primordial Helium abundance.We obtain first order corrections to the energy densities and weak interactions rates, and use them to compute the deviation in the primordial Helium abundance. After compare with observational results, a severe bound is stablished.

We study the properties of the combustion of pure neutron matter into strange matter in the framework of relativistic hydrodynamical theory of combustion. Because of the uncertainties in the actual properties of neutron matter, we employ the free neutron, Bethe-Johnson, LattimerRavenhall, and Walecka equations of state and for strange matter we adopt the MIT bag model approximation. We find that combustion is possible for free neutron, Bethe-Johnson, and LattimerRavenhall neutron matter but not for Walecka neutron matter. We interpret these results using a simple polytropic approximation showing that there exists a general flammability condition. We also study the burning of neutron matter into strange matter in a pipe showing that hydrodynamics demands flames faster than predicted by kinetics by several orders of magnitude, implying that the flame must be turbulent. Also the conditions for the deflagration to detonation transition are addressed, showing that in a pipe some of them are satisfied, strongly suggesting that the actual combustion mode should be detonation. PACS number(s): 97.60. Jd, 12.39.Ba, 95.30.L~