Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries

We investigate the symmetry properties for Baym's $\Phi$-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the $\Phi$-functional, do not fulfill the Ward-Takahashi identities of the symmetry of the underlying classical action, although the conservation laws for the expectation values of the corresponding Noether currents are fulfilled exactly for the approximation. Further we prove that one can define an effective action functional in terms of the self-consistent propagators which is invariant under the operation of the same symmetry group representation as the classical action. The requirements for this theorem to hold true are the same as for perturbative approximations: The symmetry has to be realized linearly on the fields and it must be free of anomalies, i.e., there should exist a symmetry conserving regularization scheme. In addition, if the theory is renormalizable in Dyson's narrow sense, it can be renormalized with counter terms which do not violate the symmetry.Comment: 32 papges, 3 figures, uses ReVTeX 4, V2: Added one more reference, V3: Corrected some typos, added two more sections about the large-N expansio

Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the $\phi^4$-theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the $\Phi$-derivable approximation or 2PI effective action concept.Comment: 18 pages, 7 figures Changes in version 2: Adapted title to the first paper of the series, added one figure and some references. This version was submitted to Phys. Rev. D; Changes in version 3: added one more reference Changes in version 4 (accepted for publication by Phys. Rev. D): Added a paragraph about the massless case and some remarks in the introductio

Hard gluon damping in hot QCD

The gluon collisional width in hot QCD plasmas is discussed with emphasis on temperatures near $T_c$, where the coupling is large. Considering its effect on the entropy, which is known from lattice calculations, it is argued that the width, which in the perturbative limit is given by $\gamma \sim g^2 \ln(1/g) T$, should be sizeable at intermediate temperatures but has to be small close to $T_c$. Implications of these results for several phenomenologically relevant quantities, such as the energy loss of hard jets, are pointed out.Comment: uses RevTex and graphic

Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym''s $\Phi$-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamical potential can be renormalized, in consistency with the equations of motion. This guarantees the standard $\Phi$-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation schemes to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences.Comment: 22 Pages 1 figure, uses RevTeX4. The Revision concerns the correction of some minor typos, a clarification concerning the real-time contour structure of renormalization parts and some comments concerning symmetries in the conclusions and outloo

Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a symmetric and a double well potential. We use the 2PPI formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field phi= the 2PPI formalism uses as variational parameter a time dependent mass M**2(t) which contains all local insertions into the Green function. We compare our results to those obtained in the Hartree approximation. In the symmetric Phi**4 theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in 1+1 dimensional quantum field theory there is no spontaneous symmetry breaking for T >0, and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.Comment: 14 pages, 18 encapsulated postscript figures; v2 minor changes, new appendix, accepted for publication in Phys.Rev.

The O(N) linear sigma model at finite temperature beyond the Hartree approximation

We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.Comment: 22 pages, 14 figures. v2: minor corrections, some more references. v3: added new set of data, new appendix. Submitted to Phys.Rev.

The impact of SCIAMACHY near-infrared instrument calibration on CH4 and CO total columns

The near-infrared spectra measured with the SCIAMACHY instrument on board the ENVISAT satellite suffer from several instrument calibration problems. The effects of three important instrument calibration issues on the retrieved methane (CH4) and carbon monoxide (CO) total columns have been investigated: the effects of the growing ice layer on the near-infrared detectors, the effects of the orbital variation of the instrument dark signal, and the effects of the dead/bad detector pixels. Corrections for each of these instrument calibration issues have been defined. The retrieved CH4 and CO total columns including these corrections show good agreement with CO measurements from the MOPITT satellite instrument and with CH4 model calculations by the chemistry transport model TM3. Using a systematic approach, it is shown that all three instrument calibration issues have a significant effect on the retrieved CH4 and CO total columns. However, the impact on the CH4 total columns is more pronounced than for CO, because of its smaller variability. Results for three different wavelength ranges are compared and show good agreement. The growing ice layer and the orbital variation of the dark signal show a systematic, but time-dependent effect on the retrieved CH4 and CO total columns, whereas the effect of the dead/bad pixels is rather unpredictable: some dead pixels show a random effect, some more systematic, and others no effect at all. The importance of accurate corrections for each of these instrument calibration issues is illustrated using examples where inaccurate corrections lead to a wrong interpretation of the results

Transport coefficients from the 2PI effective action

We show that the lowest nontrivial truncation of the two-particle irreducible (2PI) effective action correctly determines transport coefficients in a weak coupling or 1/N expansion at leading (logarithmic) order in several relativistic field theories. In particular, we consider a single real scalar field with cubic and quartic interactions in the loop expansion, the O(N) model in the 2PI-1/N expansion, and QED with a single and many fermion fields. Therefore, these truncations will provide a correct description, to leading (logarithmic) order, of the long time behavior of these systems, i.e. the approach to equilibrium. This supports the promising results obtained for the dynamics of quantum fields out of equilibrium using 2PI effective action techniques.Comment: 5 pages, explanation in introduction expanded, summary added; to appear in PR

Correlations of Heavy Quarks Produced at Large Hadron Collider

We study the correlations of heavy quarks produced in relativistic heavy ion collisions and find them to be quite sensitive to the effects of the medium and the production mechanisms. In order to put this on a quantitative footing, as a first step, we analyze the azimuthal, transverse momentum, and rapidity correlations of heavy quark-anti quark ($Q\overline{Q}$) pairs in $pp$ collisions at $\cal{O}$($\alpha_{s}^{3}$). This sets the stage for the identification and study of medium modification of similar correlations in relativistic collision of heavy nuclei at the Large Hadron Collider. Next we study the additional production of charm quarks in heavy ion collisions due to multiple scatterings, {\it viz.}, jet-jet collisions, jet-thermal collisions, and thermal interactions. We find that these give rise to azimuthal correlations which are quite different from those arising from prompt initial production at leading order and at next to leading order.Comment: 26 pages, 15 figures. Three new figures added, comparison to experimental data included, abstract and discussion expande

Effect of beta-adrenergic stimulation on whole-body and abdominal subcutaneous adipose tissue lipolysis in lean and obese men

AIMS/HYPOTHESIS: Obesity is characterised by increased triacylglycerol storage in adipose tissue. There is in vitro evidence for a blunted beta-adrenergically mediated lipolytic response in abdominal subcutaneous adipose tissue (SAT) of obese individuals and evidence for this at the whole-body level in vivo. We hypothesised that the beta-adrenergically mediated effect on lipolysis in abdominal SAT is also impaired in vivo in obese humans. METHODS: We investigated whole-body and abdominal SAT glycerol metabolism in vivo during 3 h and 6 h [2H5]glycerol infusions. Arterio-venous concentration differences were measured in 13 lean and ten obese men after an overnight fast and during intravenous infusion of the non-selective beta-adrenergic agonist isoprenaline [20 ng (kg fat free mass)(-1) min(-1)]. RESULTS: Lean and obese participants showed comparable fasting glycerol uptake by SAT (9.7+/-3.4 vs 9.3+/-2.5% of total release, p=0.92). Furthermore, obese participants showed an increased whole-body beta-adrenergically mediated lipolytic response versus lean participants. However, their fasting lipolysis was blunted [glycerol rate of appearance: 7.3+/-0.6 vs 13.1+/-0.9 micromol (kg fat mass)(-1) min(-1), p<0.01], as was the beta-adrenergically mediated lipolytic response per unit SAT [Delta total glycerol release: 140+/-71 vs 394+/-112 nmol (100 g tissue)(-1) min(-1), p<0.05] compared with lean participants. Net triacylglycerol flux tended to increase in obese compared with lean participants during beta-adrenergic stimulation [Delta net triacylglycerol flux: 75+/-32 vs 16+/-11 nmol (100 g tissue)(-1) min(-1), p=0.06]. CONCLUSIONS/INTERPRETATION: We demonstrated in vivo that beta-adrenergically mediated lipolytic response is impaired systematically and in abdominal SAT of obese versus lean men. This may be important in the development or maintenance of increased triacylglycerol stores and obesity