Effective field theory methods at high temperature and chemical potential

Abstract

[eng] This thesis applies and develops effective field theory methods for the study of plasmas at high temperature and/or density. In the 90s, the theoretical frameworks necessary to study quantum electrodynamics (QED) and quantum chromodynamics (QCD) in these extreme conditions were developed. The tools developed assumed that the mass of the plasma constituents could be neglected. In a first stage of the thesis, we investigate the effects of incorporating small masses associated with the fermionic constituents of the plasma in perturbative calculations, relevant when they are not extremely small compared to the temperature and/or chemical potential that characterizes the plasma. Our study provides a first step to address this impact, calculating small massive corrections to both the photon and gluon polarization tensor, under the hard thermal loop approach. To evaluate these mass corrections, we show the usefulness of effective field theories, in particular, the on-shell effective field theory (OSEFT) for fermions. Next, we analyze the impact of mass corrections in the context of energy loss due to collision of a highly massive and energetic fermion, which passes through a plasma at high temperature and/or density. Let us consider the following two cases: when the constituents of the plasma are electrons, positrons and photons, and also when these are quarks, antiquarks and gluons. Using dimensional regularization, we effectively manage the new divergences arising from the expansion by small masses and demonstrate a consistent cancellation of divergences between hard and soft contributions, obtaining a finite result. Mass corrections for energy loss are determined in the first order with logarithmic precision, extending the foundational work of Braaten and Thoma for massless fermions. In a second stage of the thesis, we develop a new effective field theory, the OSEFT for abelian gauge fields. The final Lagrangian can be formulated in terms of a gauge-invariant vector field without the need to introduce a gauge fixation term. We prove the invariance under reparameterization (RI) of the theory, which means that the Lorentz symmetry is respected. By exploiting RI symmetry, we provide a derivation from early principles of the side-jump effect for photons. We also present applications of photon OSEFT in the context of electron and positron plasmas, for example, in quantum kinetic theory and in perturbative quantum field theory calculations. In addition, we show that when considering small purely quantum effects, the classical definition of polarization ratios, given in terms of the Stokes parameters, loses its Lorentz invariance. We therefore propose a new definition of polarization ratios, which is Lorentz invariant when these small quantum effects are present, relevant in reference systems that are not at rest with respect to the medium and with possible applications in astrophysics and cosmology, where these conditions are common. Finally, we construct a quantum kinetic theory for photons in the presence of a background of axions, at the so-called collision-free limit, from the complete theory of quantum electrodynamics. We show that, in the classical regime, kinetic equations exhibit well-known features of electrodynamics with axions. The formalism we present allows us to systematically calculate how the classical limit is corrected due to small quantum effects. In addition, we address the impact of the axion background on the collective modes of photons that occur in electron and positron plasmas in thermal equilibrium. Notably, the axion background breaks the degeneration of the transverse collective modes, while the longitudinal collective mode, called plasmon, is not affected.