J. Knoll

Gapless Hartree-Fock resummation scheme for the O(N) model

A modified self-consistent Hartree-Fock approximation to the {lambda}{phi}{sup 4} theory with spontaneously broken O(N) symmetry is proposed. It preserves all the desirable features, like conservation laws and thermodynamic consistency, of the self-consistent Schwinger-Dyson scheme generated from a 2PI functional, also known as the {phi}-derivable scheme, while simultaneously respecting the Nambu-Goldstone theorem in the chiral-symmetry broken phase. Various approximate resummation schemes are discussed.

Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O ( N ) symmetry

The renormalization of a gapless {phi}-derivable Hartree-Fock approximation to the O(N)-symmetric {lambda}{phi}{sup 4} theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005).] in order to preserve all the desirable features of {phi}-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu-Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree-Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree-Fock approximation at fixed renormalization scale {mu} is discussed.

Self-consistent approach to off-shell transport

The properties of two forms of the gradient expanded Kadanoff-Baym equations, i.e., the Kadanoff-Baym and Botermans-Malfliet forms, suitable for describing the transport dynamics of particles and resonances with broad spectral widths, are discussed in context of conservation laws, the definition of a kinetic entropy, and the possibility of numerical realization. Recent results on exact conservations of charge and energy-momentum within Kadanoff-Baym form of quantum kinetics based on local coupling schemes are extended to two cases relevant in many applications. These concern the interaction via a finite-range potential and, relevant in nuclear and hadron physics, e.g., for the pion-nucleon interaction, the case of derivative coupling.

Soft Modes, Resonances and Quantum Transport ∗

Effects of the propagation of particles that have a finite lifetime and an according width in their mass spectrum are discussed in the context of transport description. First, the importance of coherence effects (Landau-Pomeranchuk-Migdal effect) on the production and absorption of field quanta in nonequilibrium dense matter is considered. It is shown that classical diffusion and Langevin results correspond to a resummation of certain field-theory diagrams formulated in terms of full nonequilibrium Greens functions. General properties of broad resonances in dense and hot systems are discussed in the framework of a self-consistent and conserving Φ-derivable method of Baym by considering the examples of the ρ meson in hadronic matter and the pion in dilute nuclear matter. Further, we address the problem of a transport description that properly takes into account the damping width of the particles. The Φ-derivable method generalized to the real-time contour provides a selfconsistent and conserving kinetic scheme. We derive a generalized expression for the nonequilibrium kinetic entropy flow, which includes corrections from fluctuations and mass-width effects. In special cases, an H theorem is proven. Memory effects in collision terms contribute to the kinetic entropy flow that, in the Fermi liquid case, reproduces the famous bosonic-type T3lnT correction to the specific heat of liquid 3He. For the example of the pion-condensate phase transition in dense nuclear matter, we demonstrate the important role of the width effects within the quantum transport.

Dynamics of resonances in strongly interacting systems

The effects of the propagation of particles which have a finite life-time and an according broad distribution in their mass spectrum are discussed in the context of a transport descriptions. In the first part some example cases of mesonic modes in nuclear matter at finite densities and temperatures are presented. These equilibrium calculations illustrate the dynamical range of spectral distributions to be adequately covered by non-equilibrium description of the dynamics of two nuclei colliding at high energies. The second part addresses the problem of transport descriptions which properly account for the damping width of the particles. A systematic and general gradient approximation is presented in the form of diagrammatic rules which permit to derive a self-consistent transport scheme from the Kadanoff-Baym equation. The scheme is conserving and thermodynamically consistent provided the self-energies are obtained within the phi-derivable two-particle irreducible (2PI) method of Baym. The merits, the limitations and partial cures of the limitations of this transport scheme are discussed in detail.

Comment on 'Nonperturbative finite T broadening of the {rho} meson and dilepton emission in heavy-ion collisions'

Our reanalysis leads us to the conclusion that the projection method introduced in [1] in order to restore the four transversality of the ρ-meson spectral function, A , suffers from serious problems with kinematical singularities. As shown below these singularities lead to a spurious and unphysical massless mode of the ρ-meson, in turn leading to a further broadening of the pion modes and through the self-consistence finally to a strong broadening of the ρ-meson. In recent studies [3, 4] the authors alternatively used the projection method introduced by two of us [6] and found a good agreement with the dimuon data of NA60 [5] on the basis of their collision-dynamic model [1]. We point out that also in this projection method there are ambiguities in the calculation.

RENORMALIZATION OF SELF-CONSISTENT Φ-DERIVABLE APPROXIMATIONS

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense and the self-consistent scheme must follow Bayms Phi-derivable concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent equations of motion. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized with the same counterterms used for the equations of motion. This guarantees the standard Phi-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation schemes. We give also a short overview over symmetry properties of the various functions defined within the 2PI scheme for the case that the underlying classical field theory has a global linearly realized symmetry.

SOFT MODES, QUANTUM TRANSPORT AND KINETIC ENTROPY

The effects of the propagation of particles which have a finite life-time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source of charged particles is studied in a classical model which can be solved completely in analytical terms. The solution corresponds to a re-summation of certain field theory diagrams. The general properties of broad resonances in dense finite temperature systems are discussed at the example of the

Resonance transport and kinetic entropy

\rho

Statistical picture of high energy nuclear collisions. [0. 5 to 1 GeV/nucleon]

-meson in hadronic matter. The second part addresses the problem of transport descriptions which also account for the damping width of the particles. The Kadanoff--Baym equation after gradient approximation together with the