The polarization tensor of neutral gluons in external fields at high temperature

The one-loop polarization operator of neutral gluons in the background constant Abelian isotopic, $H_{3}$, and hypercharge, $H_{8}$, chromomagnetic fields combined with $A_0$ electrostatic potential at high temperature is calculated. The case when $A_0=0$ is investigated separately. The proper time method is applied. It is found that neutral gluons do not acquire magnetic masses in the background fields, in contrast to the charged ones. The application of the results are discussed.Comment: 13 pages, 1 figur

The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.Comment: 45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PR

Can the scale factor be rippled?

We address an issue: would the cosmological scale factor be a locally oscillating quantity? This problem is examined in the framework of two classical 1+1-dimensional models: the first one is a string against a curved background, and the second one is an inhomogeneous Bianchi I model. For the string model, it is shown that there exist the gauge and the initial condition providing an oscillation of scale factor against a slowly evolving background, which is not affected by such an oscillation "at the mean". For the inhomogeneous Bianchi I model with the conformal time gauge, an initially homogeneous scale factor can become inhomogeneous and undergo the nonlinear oscillations. As is shown these nonlinear oscillations can be treated as a nonlinear gauge wave.Comment: 10 pages, 5 figure

Cosmological singularity as an informational seed for Everything

It is shown how to place some amount of matter into the cosmological singularity and to encode its state. A free and massless scalar field is considered, as a prototype of matter. Two different but coherent approaches to this issue are presented. The expression for the spectral energy density of the scalar particles, which is initially encoded at the singularity, is deduced. An informational aspect of the problem is discussed.Comment: 15 pages, 2 figure

Solution of the discrete Wheeler-DeWitt equation in the vicinity of small scale factors and quantum mechanics in the space of negative constant curvature

The asymptotic of the solution of the discrete Wheeler-DeWitt equation is found in the vicinity of small scale factors. It is shown that this problem is equivalent to the solution of the stationary Schr\"{o}dinger equation in the (super) space of negative constant curvature. The minimum positive eigenvalue is found from which a continuous spectrum begins.Comment: 8 page