58905616
Loop quantum gravity corrections and cosmic rays decays
Loop quantum gravity effective theories are reviewed in the context of the observed GZK limit anomaly and related processes. This is accomplished through a kinematical analysis of the modified threshold conditions for the involved decay reactions, arising from the theory. Specially interesting is the possibility of an helicity dependant violation of the limit, whose primary effect would be the observation of favoured helicity states for highly energetic particles.
55152520
On the importance of heavy fields during inflation
We study the dynamics of two-field models of inflation characterized by a hierarchy of masses between curvature and isocurvature modes. When the hierarchy is large, a low energy effective field theory (EFT) exists in which only curvature modes participate in the dynamics of perturbations. In this EFT heavy fields continue to have a significant role in the low energy dynamics, as their interaction with curvature modes reduces their speed of sound whenever the multi-field trajectory is subject to a sharp turn in target space. Here we analyze under which general conditions this EFT remains a reliable description for the linear evolution of curvature modes. We find that the main condition consists on demanding that the rate of change of the turn's angular velocity stays suppressed with respect to the masses of heavy modes. This adiabaticity condition allows the EFT to accurately describe a large variety of situations in which the multi-field trajectory is subject to sharp turns. To test this, we analyze several models with turns and show that, indeed, the power spectra obtained for both the original two-field theory and its single-field EFT are identical when the adiabaticity condition is satisfied. In particular, when turns are sharp and sudden, they are found to generate large features in the power spectrum, accurately reproduced by the EFT.
121231484
Interference in the radiation of two relativistic charges
The radiation produced by two interacting relativistic point charges is considered. Under an appropriate approximation the radiation of the system as a whole (interference effects included) is expressed as a function of the relative velocity.
119832693
Renormalized loop expansion to compute finite size effects of the constraint effective potential
In latticeφ4 close to the critical line, finite size effects can be computed by renormalized loop expansions. In order to do so, the constraint effective potential is computed to two loop order. Using this expression, we are able to extract results for renormalized masses and coupling constants from Multigrid Monte Carlo data of Mack and Meyer for the constraint effective potential close to the critical line, and compare them with the analytical results ofLüscher and Weisz. Perfect agreement is found.
119359128
Variational Study of the Phase Transition at Finite T in the $\lambda \phi^4 $-Theory
Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a stability condition for the gap-equation for the plasma mass. It shows a second order phase transition at zero temperature, in agreement with a large amount of analytical and RG analysis as well as Monte Carlo numerical evidence. As the cutoff $\Lambda $ is removed the renormalized self coupling constant $\lambda _R$ goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.
119459248
Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model
Polyakov's calculation of the effective action for the 2d nonlinear sigma-Model is generalized by purely analytic means to include contributions which are not UV-divergent and which depend on the choice of block spin. An analytic approximation to the background field which determines the classical perfect action is given, and approximations to the 1-loop correction are found. The results should be useful for numerical simulations.
1744775
Self-consistent calculation of real space renormalization group flows and effective potentials
Abstract We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method which is designed to preserve the basic stability properties of a Boltzmann factor. Particular attention is paid to controlling the errors which come from truncating the action to a manageable form. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In the first part the method is described and numerical results are presented. In the second part we discuss an improvement of the method where the saddle point approximation is preceded by self-consistent normal ordering, i.e. solution of a gap equation. In the third part we describe a general procedure to obtain higher order corrections with the help of Schwinger-Dyson equations. In this paper we treat scalar field theories as an example. The basic limitations of the method are also discussed. They come from a possible breakdown of stability which may occur when a composite block spin or block variables for domain walls would be needed.