Using generalized Nielsen identities a formal proof is given that the fermionic quasiparticle dispersion relations in a color superconductor are gauge independent. This turns out to involve gluonic tadpoles which are calculated to one-loop order in a two-flavor color superconductor. Regarding the appearance of gluon tadpoles, we argue that in QCD the color superconducting phase is automatically color neutral.

Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermiliquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading T ln T −1 term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers T (3+2n)/3 . We determine their coefficients in perturbation theory up to and including order T 7/3 and compare with exact numerical results obtained in the large-N f limit of QED and QCD. PACS numbers: 11.10.Wx, 12.38.Mh, 71.45.Gm, 11.15.Pg It has been established long ago [1] in the context of a nonrelativistic electron gas that the only weakly screened low-frequency transverse gauge-boson interactions lead to a qualitative deviation from Fermi liquid behavior. A particular consequence of this is the appearance of an anomalous contribution to the low-temperature limit of entropy and specific heat proportional to αT ln T −1 [1, 2, 3], but it was argued that the effect would be probably too small for experimental detection.More recently, it has been realized that analogous non-Fermi-liquid behavior in ultradegenerate QCD is of central importance to the magnitude of the gap in color superconductivity [4,5,6], and it has been pointed out [7] that the anomalous contributions to the low-temperature specific heat may be of interest in astrophysical systems such as neutron or protoneutron stars, if they involve a normal (non-superconducting) degenerate quark matter component.So far only the coefficient of the αT ln T −1 term in the specific heat has been determined (with Ref.[3] correcting the result of Ref.[1] by a factor of 4), but not the complete argument of the leading logarithm. While the existence of the T ln T −1 term implies that there is a temperature range where the entropy or the specific heat exceeds the ideal-gas value, without knowledge of the constants "under the log" it is impossible to give numerical values for the required temperatures.Furthermore, a quantitative understanding of these anomalous contributions is also of interest with regard to the recent progress made in high-order perturbative calculations of the pressure (free energy) of QCD at nonzero temperature and chemical potential [8], where it has been found that dimensional reduction techniques work remarkably well except for a narrow strip in the T -µ-plane around the T = 0 line.In the present Letter we report the results of a calculation of the low-temperature entropy and specific heat for ultradegenerate QED and QCD which goes beyond the leading log approximation. Besides completing the leading logarithm, we find that for T /µ ≪ g ≪ 1, where g is either the strong or the electromagnetic coupling constant, the higher terms of the low-temperature series involve also anomalous fractional powers T (3+2n)/3 , and we give their coefficients through order T 7/3 . Our starting point is an expression for the thermodynamic potential of QED and QCD

We determine the dispersion relations of fermionic quasiparticles in ultradegenerate plasmas by a complete evaluation of the on-shell hard-dense-loop-resummed one-loop fermion self energy for momenta of the order of the Fermi momentum and above. In the case of zero temperature, we calculate the nonanalytic terms in the vicinity of the Fermi surface beyond the known logarithmic approximation, which turn out to involve fractional higher powers in the energy variable. For nonzero temperature (but much smaller than the chemical potential), we obtain the analogous expansion in closed form, which is then analytic but involves polylogarithms. These expansions are compared with a full numerical evaluation of the resulting group velocities and damping coefficients.

We compute the low-temperature behavior of the specific heat of normal (non-color-superconducting) degenerate quark matter as well as that of an ultradegenerate electron gas. Long-range magnetic interactions lead to non-Fermi-liquid behavior with an anomalous leading T lnT ÿ1 term. Depending on the thermodynamic potential used as a starting point, this effect appears as a consequence of the logarithmic singularity in the fermion self-energy at the Fermi surface or directly as a contribution from the only weakly screened quasistatic magnetic gauge bosons. We show that a calculation of Boyanovsky and de Vega claiming the absence of a leading T lnT ÿ1 term missed it by omitting vector boson contributions to the internal energy. Using a formulation which collects all nonanalytic contributions in bosonic ring diagrams, we systematically calculate corrections beyond the well-known leading-log approximation. The higher-order terms of the low-temperature expansion turn out to also involve fractional powers T 32n=3 and we explicitly determine their coefficients up to and including order T 7=3 as well as the subsequent logarithmically enhanced term T 3 lnc=T. We derive also a harddense-loop resummed expression which contains the infinite series of anomalous terms to leading order in the coupling and which we evaluate numerically. At low temperatures, the resulting deviation of the specific heat from its value in naive perturbation theory is significant in the case of strongly coupled normal quark matter and thus of potential relevance for the cooling rates of (proto)neutron stars with a quark matter component.

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