Non-vanishing Chemical Potential Research Articles

Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general $\xi$ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge invariant analytical expressions for the dispersion relations.

Braaten-Pisarski method at finite chemical potential

The effective perturbation theory developed by Braaten and Pisarski for gauge theories at finite temperature is extended to finite chemical potential. As a first application the collisional energy loss of a heavy quark propagating through a quark-gluon plasma with non-vanishing quark chemical potential is considered. Assuming μ T ⋍ 1 , motivated by numerical simulations of heavy ion collisions at RHIC energies, we find that the effect of the quark chemical potential is rather small, unless the energy density instead of the temperature is fixed.

Fermion and antifermion effective masses in high temperature gauge theories in a CP-asymmetric background.

We calculate the splitting between fermion and antifermion effective masses in high temperature gauge theories in the presence of a nonvanishing chemical potential due to the $\mathrm{CP}$-asymmetric fermionic background. In particular we consider the case of left-handed leptons in the SU(2)\ensuremath{\bigotimes}U(1) theory when the temperature is above 250 GeV and the gauge symmetry is restored.

Finite temperature and chemical potentials in higher dimensions

The finite-temperature 1-loop effective potential for scalar and spinor fields on a Kaluza-Klein spacetime M4*VN is calculated using zeta-function regularization in the presence of a nonvanishing chemical potential. Both high- and low-temperature expansions are derived and the role of the zero modes is discussed.

Is the number of photons conserved in an expanding universe?

A Friedman-like scenario is described in which due to the direct coupling of electromagnetic fields to spacetime curvature-the total number of photons comprised in the Universe at a given epoch changes as the Universe expands. The photon number distribution function, according to this scenario, acquires an explicit dependence on a non-vanishing chemical potential term which accounts for the occurrence of tidal effects in the interaction of photons (which, in a gravitational field, should not be treated as idealised, point-like objects) with gravity. The total amount of entropy observed today may be reviewed from a new perspective and ipso facto explained away.

Phase transition in a nucleon-antinucleon system.

We have examined the phase structure of a nucleon-antinucleon plasma in Walecka's relativistic mean-field approximation originally due to Theis et al. who have shown that the nuclear-matter system exhibits a phase transition at ${T}_{c}$\ensuremath{\simeq}200 MeV for zero baryon density. It is found that the inclusion of a small nonvanishing chemical potential which, in turn, implies a nonzero baryon density does not negate this result.

Phase transition of a fermionic system in a gauge theory.

The nature of possible transitions in the heat capacity of a fermionic system in a spontaneously broken gauge theory is studied. It is shown that the heat capacity shows a first-order discontinuous behavior at the critical temperature as the symmetry restoration shows a smooth or discontinuous transition near the critical value. The effects of quantum fluctuations leading to temperature dependence in the masses of scalar and vector mesons on the fermionic heat capacity are also considered. Finally, the consequences of the inclusion of nonvanishing chemical potential in the system are briefly discussed.

Two-point Green's functions in quantum electrodynamics at finite temperature and density

One-particle propagators of the relativistic electron-positron gas are systematically investigated. With the nonvanishing chemical potential the neutrality of the whole system is secured by a uniformly charged classical background described by a classical current J μ . Due to the translational invariance of this model it is natural to investigate the properties of the propagators in the momentum space. The Fourier-transforms of the Green's functions have been expressed in terms of the generalized spectral Lehmann representation and the second-order spectral functions of the photon and electron propagators have been found. The matter-dependent part of the propagator is finite and only the vacuum part has to be renormalized with the use of standard renormalization counterterms. The singularities of the gauge-independent photon propagator have been further investigated with the use of the spectal representation and nonperturbative expressions for the spectrum of collective excitations have been obtained. In the second order of perturbation they reproduce the asymptotic formulas at T → 0 and T → ∞ cited previously in the literature. In particular, the relativistic plasma frequency (photon effective mass) has been expressed in a simple form in terms of the integrals over the spectral functions. Our formulas for the relativistic plasmon mass squared Ω 2 exhibit an interesting property that at some temperature and density Ω 2 should become negative. However, simple estimates show that this phenomenon occurs at highly nonrealistic temperatures of the order of e 137, i.e., in the region where the perturbation theory fails. The damping of the collective excitations is also considered.

Roton second sound in the relaxation-time approximation

In the hydrodynamic limit the Boltzmann equation for rotons is solved in the relaxation-time approximation with two relaxation times. One of them characterizes the approach of the system to a local equilibrium with constant and zero chemical potential (the collisions between the elementary excitations do not conserve total number), whereas the other one scales the approach to a local equilibrium with nonvanishing chemical potential (total number conserved). The solution is used to investigate the velocity and the attenuation of second sound. The velocity is found to change as a function of the second-sound frequency from a value of $\frac{\sqrt{3}kT}{{p}_{0}}$ at frequencies which are slow compared to the frequency of number-nonconserving collisions to a value of $\frac{3kT}{{p}_{0}}$ in the opposite limit. ${p}_{0}$ is the momentum at the roton minimum. The corresponding attenuation displays a maximum in the region of steepest change of the velocity.