Critical phenomena from the two-particle irreducible 1/N expansion

The 1/N expansion of the two-particle irreducible (2PI) effective action is employed to compute universal properties at the second-order phase transition of an O(N)-symmetric N-vector model directly in three dimensions. At next-to-leading order the approach cures the spurious small-N divergence of the standard (1PI) 1/N expansion for a computation of the critical anomalous dimension eta(N), and leads to improved estimates already for moderate values of N.Comment: 18 pages, 3 figure

QED Electrical Conductivity using the 2PI Effective Action

In this article we calculate the electrical conductivity in QED using the 2PI effective action. We use a modified version of the usual 2PI effective action which is defined with respect to self-consistent solutions of the 2-point functions. We show that the green functions obtained from this modified effective action satisfy ward identities and that the conductivity obtained from the kubo relation is gauge invariant. We work to 3-loop order in the modified 2PI effective action and show explicitly that the resulting expression for the conductivity contains the square of the amplitude that corresponds to all binary collision and production processes.Comment: 24 pages, 21 figure

Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields

Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by the Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for the Boltzmann equation.Comment: text and figures revised, references added, results unchanged, 21 pages, 10 figures, published in Phys. Rev. D73 (2006) 12500

Non perturbative renormalization group and momentum dependence of n-point functions (II)

In a companion paper (hep-th/0512317), we have presented an approximation scheme to solve the Non Perturbative Renormalization Group equations that allows the calculation of the $n$-point functions for arbitrary values of the external momenta. The method was applied in its leading order to the calculation of the self-energy of the O($N$) model in the critical regime. The purpose of the present paper is to extend this study to the next-to-leading order of the approximation scheme. This involves the calculation of the 4-point function at leading order, where new features arise, related to the occurrence of exceptional configurations of momenta in the flow equations. These require a special treatment, inviting us to improve the straightforward iteration scheme that we originally proposed. The final result for the self-energy at next-to-leading order exhibits a remarkable improvement as compared to the leading order calculation. This is demonstrated by the calculation of the shift $\Delta T_c$, caused by weak interactions, in the temperature of Bose-Einstein condensation. This quantity depends on the self-energy at all momentum scales and can be used as a benchmark of the approximation. The improved next-to-leading order calculation of the self-energy presented in this paper leads to excellent agreement with lattice data and is within 4% of the exact large $N$ result.Comment: 35 pages, 11 figure

Incommensurate antiferromagnetic fluctuations in the two-dimensional Hubbard model

Commensurate and incommensurate antiferromagnetic fluctuations in the two-dimensional repulsive t-t'-Hubbard model are investigated using functional renormalization group equations. For a sufficient deviation from half filling we establish the existence of local incommensurate order below a pseudocritical temperature T_{pc}. Fluctuations not accounted for in the mean field approximation are important--they lower T_{pc} by a factor \approx2.5.Comment: 7 pages, 8 figures, some changes due to referees' comments, equivalent to published versio

Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium

Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. In contrast to this standard Boltzmann equations cannot describe the process of quantum-chemical equilibration, and consequently also cannot feature the above separation of time scales.Comment: 17 pages, 8 figures, REVTeX

Baryon Asymmetry of the Universe without Boltzmann or Kadanoff-Baym

We present a formalism that allows the computation of the baryon asymmetry of the universe from first principles of statistical physics and quantum field theory that is applicable to certain types of beyond the Standard Model physics (such as the neutrino Minimal Standard Model -- $\nu$MSM) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of Standard Model particles is very weakly coupled to a new sector (sterile neutrinos in the $\nu$MSM case) that is out-of-equilibrium. The key point that allows a computation without kinetic equations is that the number of sterile neutrinos produced during the relevant cosmological period remains small. In such a case, it is possible to expand the formal solution of the von Neumann equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose a toy model (containing only two active and two sterile neutrinos) to illustrate the use of the formalism, but it could be applied to other models.Comment: 26 pages, 10 figure

Ward identities for the Anderson impurity model: derivation via functional methods and the exact renormalization group

Using functional methods and the exact renormalization group we derive Ward identities for the Anderson impurity model. In particular, we present a non-perturbative proof of the Yamada-Yosida identities relating certain coefficients in the low-energy expansion of the self-energy to thermodynamic particle number and spin susceptibilities of the impurity. Our proof underlines the relation of the Yamada-Yosida identities to the U(1) x U(1) symmetry associated with particle number and spin conservation in a magnetic field.Comment: 8 pages, corrected statements about infintite flatband limi

Scattering in an environment

The cross section of elastic electron-proton scattering taking place in an electron gas is calculated within the Closed Time Path method. It is found to be the sum of two terms, one being the expression in the vacuum except that it involves dressing due to the electron gas. The other term is due to the scattering particles-electron gas entanglement. This term dominates the usual one when the exchange energy is in the vicinity of the Fermi energy. Furthermore it makes the trajectories of the colliding particles more consistent and the collision more irreversible, rendering the scattering more classical in this regime.Comment: final version to appear in Phys. Rev.

Preheating with Trilinear Interactions: Tachyonic Resonance

We investigate the effects of bosonic trilinear interactions in preheating after chaotic inflation. A trilinear interaction term allows for the complete decay of the massive inflaton particles, which is necessary for the transition to radiation domination. We found that typically the trilinear term is subdominant during early stages of preheating, but it actually amplifies parametric resonance driven by the four-legs interaction. In cases where the trilinear term does dominate during preheating, the process occurs through periodic tachyonic amplifications with resonance effects, which is so effective that preheating completes within a few inflaton oscillations. We develop an analytic theory of this process, which we call tachyonic resonance. We also study numerically the influence of trilinear interactions on the dynamics after preheating. The trilinear term eventually comes to dominate after preheating, leading to faster rescattering and thermalization than could occur without it. Finally, we investigate the role of non-renormalizable interaction terms during preheating. We find that if they are present they generally dominate (while still in a controllable regime) in chaotic inflation models. Preheating due to these terms proceeds through a modified form of tachyonic resonance.Comment: 19 pages, 10 figures, refs added, published versio