Study of the standard model for elementary particles at the finite temperature

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(1) The pinch technique (PT) is applied to obtain the gauge-independent resummed gluon self-energy in a hot Yang-Mills gas. The effective gluon self-energy, which is obtained as the sum of the resummed gluon self-energy and the resummed pinch contributions, is not only gauge-independent but also satisfies the transversality relation. Using this gauge-independent effective gluon self-energy, we calculate the damping rate for transverse gluons in the leading order and show that the result coincides with the one obtained by Braaten and Pisarski.(2) It is shown in the framework of the operator product expansion and the renormalization group method that the twist-3 part of flavor nonsinglet spin structure function g_2(x, Q^2) of nucleon obeys a simple Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation in the large N_C limit even in the case of massive quarks (N_C is the number of colours).(3) The virtual photon structure function g_1^<gamma> (x, Q^2, P^2), which can be obtained in polarized e^+ +e^- & colliding-beam experiments, is investigated for LAMBDA^2>>P^2>>Q^2, where -Q^2 (-P^2) is the mass squared of the probe (target) photon. The analysis is made to next-to-leading order in QOD, in the framework of the QCD improved parton model with the DGLAP evolution equations. The non-leading corrections significantly modify the leading log result, in particular, at large x as well as at small x.