| dc.description.abstract | Quark-gluon plasma is believed to have existed in the initial moments after the Big Bang. Investigating the phase transition of hadronic matter is an essential part of studying the early universe and the behavior of matter under extreme conditions. At lower temperatures and densities, quarks and gluons exist together in a tightly bound hadronic state. However, at higher temperatures
(150–200 MeV) or at densities much greater than nuclear matter, such as those present in the early universe or in heavy-ion collisions, hadronic matter undergoes a phase transition. During this transition, hadronic matter transforms into quark-gluon plasma, where quarks and gluons are no longer confined. Developing the equation of state through various frameworks helps us understand and predict the behavior of QGP under different conditions. In thermodynamics and statistical mechanics, the equation of state (EoS) describes the relationship between various thermodynamic variables, such as pressure, temperature, and volume, for a given system. Several potential models are used to develop the EoS to describe the properties of quark matter. In the fields of high-energy
nuclear physics and astrophysics, these studies are of great significance.Our work encompasses three primary areas: (1) Deriving an equation of state for Quark-Gluon Plasma (QGP) in the presence of a magnetic field. (2) Investigating cold deconfined matter at zero Kelvin with a focus on the magnetic field’s influence. (3) Deriving and evaluating the temperature-dependent coupling constant for the φ 4 theory.We developed a modified liquid drop potential model to explore the thermo-dynamics of quark-gluon plasma (QGP) above the critical temperature, both in the absence and presence of a magnetic field. The model follows Mayer’s cluster expansion procedure. In this model, quarks and gluons are described as quasiparticles whose behavior is influenced by the QGP medium. Remarkably, even at temperatures below the critical temperature (T < T c ), the equation of state for pressure and energy density across 2, 2+1, and 3 flavors demonstrates a strong agreement with lattice data at zero magnetic field. Also, this modified
liquid drop model is in good agreement with lattice data for magnetized quark- gluon plasma in the region T > 113 MeV.In (2), building upon prior work on cold deconfined matter, we have incorporated the influence of a magnetic field. Employing standard statistical mechanics procedures, we have adapted integrals to the magnetic field environment. Analytical equations for number density, energy density, and pressure are derived. This work extends our understanding of the interplay between extreme conditions and quark matter.The final part of our thesis focuses on deriving a temperature-dependent coupling constant for the φ 4 theory. Using the imaginary time formalism in thermal field theory, we derive the running coupling constant and running mass in two loop order. In the process, we express the imaginary time formalism of Feynman diagrams as the summation of nonthermal quantum field theory (QFT) Feynman diagrams with coefficients that depend on temperature and mass. Renormalization constants for thermal φ 4 theory were derived using simple diagrammatic analysis. Our model links the nonthermal QFT and the imaginary time formalism by assuming both have the same mass scale μ and coupling constant g. When these results are combined with the renormalization group equations and applied simultaneously to thermal and nonthermal proper vertex functions, the coupling constant and running mass with implicit temperature dependence are obtained. We evaluated pressure for scalar particles in two loop orders at the zero external momentum limit by substituting the running mass result in the quasiparticle model. We successfully obtained a running coupling constant for the φ 4 theory. A noteworthy aspect of our work is the development of the “SMC” technique (Same Mass scale and Coupling), allowing the simultaneous solution of two renormalization groups of equations. | en_US |
