Browsing by Subject "thermal field theory"

We study a system of cold high-density matter consisting purely of quarks and gluons. The mathematical construction of Quantum Chromodynamics (QCD) introduces interactions between the fields, which modify the thermodynamic properties of the system. In the presence of interactions, we can not solve the thermodynamic properties of the system analytically. The method is to expand the result in a series in terms of the QCD coupling constant. This is referred to as the perturbation theory in the context of thermal field theory (TFT). The coupling constant describes the strength of the interaction. We introduce the basic calculation methods used in the QCD and the TFTs in general. We will also include the chemical potential associated with the number of quarks in the system in the calculation. In the case of zero temperature, quarks form a Fermi-sphere such that energy states lower than the chemical potential will be Pauli blocked. The resulting fermionic momentum integrals are modified as a consequence. We can split these integrals into two parts, referred to as the vacuum and matter parts. We can split the calculation of the pressure into two distinct contributions: one from skeleton diagrams and one from ring diagrams. The ring diagrams have unphysical IR divergences that we can not cancel using the counterterms. This is why hard thermal loop (HTL) effective field theory (EFT) is introduced. We will discuss this HTL framework, which requires the computation of the matter part of the gluon polarization tensor, which we will also evaluate in this thesis.

We determine the leading thermal contributions to various self-energies in finite-temperature and -density quantum chromodynamics (QCD). The so-called hard thermal loop (HTL) self-energies are calculated for the quark and gluon fields at one-loop order and for the photon field at two-loop order using the real-time formulation of thermal field theory. In-medium screening effects arising at long wavelengths necessitate the reorganization of perturbative series of thermodynamic quantities. Our results may be directly applied in a reorganization called the HTL resummation, which applies an effective theory for the long-wavelength modes in the medium. The photonic result provides a partial next-to-leading order correction to the current leading-order result and can be later extended to pure QCD with the techniques we develop. The thesis is organized as follows. First, by considering a complex scalar field, we review the main aspects of the equilibrium real-time formalism to build a solid foundation for our thermal field theoretic calculations. Then, these concepts are generalized to QCD, and the properties of the QCD self-energies are thoroughly studied. We discuss the long-wavelength collective behavior of thermal QCD and introduce the HTL theory, outlining also the main motivations for our calculations. The explicit computations of self-energies are presented in extensive detail to highlight the computational techniques we employ.

Astronomical observations suggest that the cores of neutron stars may have high enough baryon densities to contain quark matter (QM). The unavailability of lattice field theory makes perturbative computations important for understanding the thermodynamics of quantum chromodynamics at high baryon densities. The gluon self-energy contributes to many transport coefficients in QM, such as thermal conductivity and shear viscosity, through quark-quark scattering processes. The contribution of short-wavelength virtual gluons to the self-energy of soft, long-wavelength gluons, known as the hard-thermal-loop (HTL) self-energy, was recently computed at next-to-leading order (NLO) in perturbation theory. In this thesis, we complete the evaluation of the NLO self-energy of soft gluons in cold QM by computing the contribution from soft virtual gluons, known as the one-loop HTL-resummed self- energy. We use HTL effective theory, a reorganization of the perturbative series for soft gluons, within the imaginary-time formulation of thermal field theory. We present the result in terms of elementary functions and finite integrals that can be evaluated numerically. We show explicitly that the NLO self-energy is finite and gauge dependent. The NLO self-energy could be used to compute corrections to transport coefficients in cold QM, which may be relevant for neutron-star applications.