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At so high temperature (T) that the coupling constant (g) is small and themasses of the particles are negligible, different scheme has to be applied ineach energy scale in the analysis of the quark-gluon plasma (QGP). In the softenergy region (p gT), the simple perturbative expansion called the hard thermalloop (HTL) approximation can be applied, and that approximation expects theexistence of the bosonic and fermionic collective excitations called plasmonand plasmino. On the other hand, in the ultrasoft energy region (p g^2T), theHTL approximation is inapplicable due to infrared singularity, so the questionwhether there are any excitation modes in that energy region has not beenstudied well. In this thesis, we analyze the quark spectrum whose energy isultrasoft in QGP, using the resummed perturbation theory which enables us tosuccessfully regularize the infrared singularity. Since the Yukawa model andQED are simpler than QCD but have some similarity to QCD, we also work in thesemodels. As a result, we establish the existence of a novel fermionic mode inthe ultrasoft energy region, and obtain the expressions of the pole positionand the strength of that mode. We also show that the Ward-Takahashi identity issatisfied in the resummed perturbation theory in QED/QCD. Furthermore, wederive the linearized and generalized Boltzmann equation for the ultrasoftfermion excitations in the Kadanoff-Baym formalism, and show that the resultantequation is equivalent to the self-consistent equation in the resummedperturbation theory. We also derive the equation which determines the n-pointfunctions with external lines for a pair of fermions and (n-2) bosons withultrasoft momenta, by considering the non-linear response regime using thegauge symmetry. We also derive the Ward-Takahashi identity from theconservation law of the electromagnetic current in the Kadanoff-Baym formalism.

Diagrammatic and Kinetic Equation Analysis of Ultrasoft Fermionic Sector in Quark-Gluon Plasma