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Cold quark matter in perturbative QCD

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Title: Cold quark matter in perturbative QCD
Author(s): Nurmela, Mika
Contributor: University of Helsinki, Faculty of Science
Degree program: Master 's Programme in Theoretical and Computational Methods
Specialisation: Theoretical Physics
Language: English
Acceptance year: 2022
Abstract:
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.
Keyword(s): quantum chromodynamics thermal field theory hard thermal loop gluon self-energy


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