(Non)-Abelian gauge field theories of the Fermi gas. Neutron-quark stars

It is indicated that the ground state of Fermi systems with (non)-Abelian gauge interactions has a well defined quantum theory devoid of infrared divergences and mass singularities. This is exploited to develop a systematic quantum theory of the quark gas. The equation of state of the quark gas is evaluated up to second order in the Gell-Mann-Low charge α_S(μ). The analysis based on neutron matter models suggests that the matter in the neutron stars can be in the quark phase provided the color interaction is “moderately” strong i.e. α_S (3 GeV) ? 0.3.     

Screening of instantons in the quark gas

The grand partition function of quark matter is developed about an arbitrary classical gauge field configuration in a systematic weak coupling expansion. In the presence of a finite density massless quark gas the instanton induced effective quark interaction is modified by a factor exp[?2N_F(ω?)²], i.e. the baryon number chemical potential μ acts as an intrinsic infrared cutoff on the instanton scale size ?. The equation of state of the quark matter is also briefly discussed.     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.