arXiv subjects
Publications and source records attributed to Christof Wetterich.
The CMB data recently released by BOOMERANG and MAXIMA suggest that the anisotropy spectrum has a third peak in the range 800 1 are disfavoured. Models with more than 5% quintessence before last scattering require a spectral index greater than 1. These constraints are compared with supernovae observations. We also show that the CMB alone now provides strong evidence for an accelerating universe.
A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the renormalization flow of scalar bound states which are formed out of fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge coupling as an example. Thereby, the notions of bound state or fundamental particle become scale dependent, being classified by the fixed-point structure of the flow of effective couplings.
We discuss the influence of dark energy on structure formation, especially the effects on σ_8. Our interest is particularly focused on quintessence models with time-dependent equation of state and non-negligible quintessence component in the early universe. We obtain an analytic expression for σ_8 valid for a large class of dark energy models. We conclude that structure formation is a good indicator for the history of dark energy and use our results to set constraints on quintessence models.
We compute the correlation functions for antiferromagnetic and d-wave superconducting fermion bilinears in a generalized mean field type approximation for the Hubbard model. For high temperature our explicit expressions show that homogeneous field configurations are preferred for these composite bosons. Below a critical temperature we find spontaneous symmetry breaking with homogeneous expectation values of the composite fields. Our results can be used to device a nonperturbative flow equation for the exploration of the low temperature regime.
A hypothetical dark energy component may have an equation of state that is different from a cosmological constant and possibly even changing in time. The spacing of the cosmic microwave background peaks is sensitive to the ratio of the horizon sizes today and at last scattering and therefore to the details of the cosmological evolution. Together with independent measurements of today's cosmological parameters, this restricts quintessence models in the epoch before and during decoupling. For fixed Ω^b_0, Ω^{cdm}_0 and h, we give an analytic estimate of the spacing that depends on Ω^ϕ_{ls}, Ω^ϕ_0 and an effective equation of state of the dark energy component.
We propose that it should be possible to use the CMB to discriminate between dark energy models with different equations of state, including distinguishing a cosmological constant from many models of quintessence. The separation of peaks in the CMB anisotropies can be parametrised by three quantities: the amount of quintessence today, the amount at last scattering, and the averaged equation of state of quintessence. In particular, we show that the CMB peaks can be used to measure the amount of dark energy present before last scattering.
A nonperturbative renormalization group equation describes how the momentum dependent four-quark vertex depends on an infrared cutoff. We find a quasilocal one-particle irreducible piece generated by (anomaly-free) multi-gluon exchange. It becomes important at a cutoff scale where scalar and pseudoscalar meson-bound states are expected to play a role. This interaction remains subleading as compared to the effective one-gluon exchange contribution. The local instanton induced four-quark interaction becomes dominant at a scale around 800 MeV. In absence of a gluon mass the strong dependence of the one-gluon exchange on the transferred momentum indicates that the pointlike interactions of the Nambu-Jona-Lasinio model cannot give a very accurate description of QCD. A pointlike effective four-quark interaction becomes more realistic in case of spontaneous color symmetry breaking.
Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These truncation schemes can be implemented equally well in a classical statistical system, where results can be tested by comparison with the complete nonlinear evolution obtained by numerical methods. For a 1+1 dimensional scalar field we find that the early-time behaviour is reproduced qualitatively by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the fixed point, the full nonlinear evolution shows thermalization with a (surprisingly) slow relaxation.
The phase transitions of liquid Helium 3 are described by truncations of an exact nonperturbative renormalization group equation. The location of the first order transition lines and the jump in the order parameter are computed quantitatively. At the triple point we find indications for partially universal behaviour. We suggest experiments that could help to determine the effective interactions between fermion pairs.
The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of translationally invariant expectation values for colored composite scalar fields. A suitable mean field approximation for the two dimensional colored Hubbard model shows indeed phases with antiferromagnetic ordering or d-wave superconductivity at low temperature. At low enough temperature the transition to the antiferromagnetic phase is of first order. The present formulation also allows an easy extension to more complicated microscopic interactions.
Thermalization of classical fields is investigated in a ϕ^4 scalar field theory in 1+1 dimensions, discretized on a lattice. We numerically integrate the classical equations of motion using initial conditions sampled from various nonequilibrium probability distributions. Time-dependent expectation values of observables constructed from the canonical momentum are compared with thermal ones. It is found that a closed system, evolving from one initial condition, thermalizes to high precision in the thermodynamic limit, in a time-averaged sense. For ensembles consisting of many members with the same energy, we find that expectation values become stationary - and equal to the thermal values - in the limit of infinitely many members. Initial ensembles with a nonzero (noncanonical) spread in the energy density or other conserved quantities evolve to noncanonical stationary ensembles. In the case of a narrow spread, asymptotic values of primary observables are only mildly affected. In contrast, fluctuations and connected correlation functions will differ substantially from the canonical values. This raises doubts on the use of a straightforward expansion in terms of 1PI-vertex functions to study thermalization.
We investigate the time evolution of a classical ensemble of isolated periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based on an exact evolution equation for the time dependence of correlation functions. We discuss its solutions in an approximation which retains all contributions in next-to-leading order in a 1/N expansion and preserves time reflection symmetry. We observe effective irreversibility and approximate thermalization. At large time the system approaches stationary solutions in the vicinity of, but not identical to, thermal equilibrium. The ensemble therefore retains some memory of the initial condition beyond the conserved total energy. Such a behavior with incomplete thermalization is referred to as "mesoscopic dynamics". It is expected for systems in a small volume. Surprisingly, we find that the nonthermal asymptotic stationary solutions do not change for large volume. This raises questions on Boltzmann's conjecture that macroscopic isolated systems thermalize.
The QCD-vacuum is characterized by the Higgs phenomenon for colored scalar fields. In this dual picture the gluons appear as the octet of vector mesons. Also quarks and baryons are identified. Gluon-meson and quark-baryon duality can account in a simple way for realistic masses of all low-mass hadrons and for their interactions.
We investigate the non-equilibrium properties of an N-component scalar field theory. The time evolution of the correlation functions for an arbitrary ensemble of initial conditions is described by an exact functional differential equation. In leading order in the 1/N expansion the system can be understood in terms of infinitely many conserved quantities. They forbid the approach to the canonical thermal distribution. Beyond leading order only energy conservation is apparent generically. Nevertheless, we find a large manifold of stationary distributions both for classical and quantum fields. They are the fixed points of the evolution equation. For small deviations of the correlation functions from a large range of fixed points we observe stable oscillations. These results raise the question of if and in what sense the particular fixed point corresponding to thermal equilibrium dominates the large time behavior of the system.
We compute the momentum dependence of the effective four quark interaction in QCD after integrating out the gluons. Our method is based on a truncation of exact renormalization group equations which should give reasonable results for momenta above the confinement scale. The difference between the four quark interaction and the heavy quark potential can be minimized for an optimal renormalization scheme in Landau gauge. Within the momentum range relevant for quarkonia our results agree with phenomenological potentials. We also calculate the propagators for gluons and ghosts in Landau-gauge.
Existence and properties of the electroweak phase transition in the early universe depend strongly on the mass of the Higgs scalar M_H. There is presumably no true symmetry restoration at high temperature. Nevertheless, a first order phase transition occurs in the standard model for M_H smaller than about 70 GeV. For a realistic scalar mass M_H larger than about 70 GeV the transition to the high temperature regime is described by a crossover, due to the strong electroweak gauge interactions for temperatures near and above the critical temperature. Electroweak baryogenesis during this transition seems not possible within the standard model. The observed baryon asymmetry in the universe therefore implies the necessity of an extension of the standard model.
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably averaged quantities or for subsystems, similar to quantum statistics. The classical time evolution of correlation functions shows many dynamical features of quantum mechanics.
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics and the approach to equilibrium without the need of solving the nonlinear microscopic equations of motion or computing the time dependence of the probability distribution explicitly.