14281658
A self consistent study of the phase transition in the scalar electroweak theory at finite temperature
We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two — step method. It combines i) dimensional reduction to a 3 — dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations.
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.
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.
8354557
Cluster Algorithm Renormalization Group Method
We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We ill ustrate it by means of the 2D Ising model. We compute the critical exponents ν and η and the renormalization group flow of the probability density function of the magnetization. The results, compared to the standard Monte Carlo Renormalization Group proposed by Swendsen [1], are very accurate and the method works faster by a factor which grows monotonically with the lattice size. This allows to simulate larger lattices in reachable computational times.
119486225
Resonance enhancement of particle production during reheating
We found a consistent equation of reheating after inflation which shows that for small quantum fluctuations the frequencies of resonance are slighted different from the standard ones. Quantum interference is taken into account and we found that at large fluctuations the process mimics very well the usual parametric resonance, but proceeds in a different dynamical way. The analysis is made in a toy quantum mechanical model and we discuss further its extension to quantum field theory.
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.
119299896
Mass hierarchies and non-decoupling in multi-scalar field dynamics
In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these non-decoupled degrees of freedom and deduce its non-trivial contribution to the low energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory.
54968209
Loop quantum gravity and ultrahigh energy cosmic rays
it has been suggested that quantum-gravitational effects may be playing a decisive role in the propagation of ultrahigh energy cosmic rays. In this article we take the loop quantum gravity approach. We shall provide some techniques to establish and analyze new constraints on the loop quantum gravity parameters arising from both sets of data, HiRes and AGASA. We shall also study their effects on the predicted spectrum for ultrahigh energy cosmic rays. As a result we will state the possibility of reconciling the AGASA observations.
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.
119475712
Confining the electroweak model to a brane
We introduce a simple scenario where, by starting with a five-dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of fermions is generated by the nontrivial topological solution of a SU(3) scalar field. The 4-D fermions are found to be chiral, and to have interesting properties coming from their 5-D group representation structure. The gauge fields, on the other hand, are localized by loop corrections taking place at the branes produced by the fermions. We show that these two confining mechanisms can be put together to reproduce the basic structure of the electroweak model for both leptons and quarks. A few important results are: Gauge and Higgs fields are unified at the 5-D level; and new fields are predicted: One left-handed neutrino with zero-hypercharge, and one massive vector field coupling together the new neutrino with other left-handed leptons. The hierarchy problem is also addressed.
118586772
Features of heavy physics in the CMB power spectrum
The computation of the primordial power spectrum in multi-field inflation models requires us to correctly account for all relevant interactions between adiabatic and non-adiabatic modes around and after horizon crossing. One specific complication arises from derivative interactions induced by the curvilinear trajectory of the inflaton in a multi-dimensional field space. In this work we compute the power spectrum in general multi-field models and show that certain inflaton trajectories may lead to observationally significant imprints of `heavy' physics in the primordial power spectrum if the inflaton trajectory turns, that is, traverses a bend, sufficiently fast (without interrupting slow roll), even in cases where the modes normal to the trajectory have masses approaching the cutoff of our theory. We emphasize that turning is defined with respect to the geodesics of the sigma model metric, irrespective of whether this is canonical or non-trivial. The imprints generically take the form of damped superimposed oscillations on the power spectrum. In the particular case of two-field models, if one of the fields is sufficiently massive compared to the scale of inflation, we are able to compute an effective low energy theory for the adiabatic mode encapsulating certain relevant operators of the full multi-field dynamics. As expected, a particular characteristic of this effective theory is a modified speed of sound for the adiabatic mode which is a functional of the background inflaton trajectory and the turns traversed during inflation. Hence in addition, we expect non-Gaussian signatures directly related to the features imprinted in the power spectrum.