  The thesis contains studies of properties quark-gluon plasma, using some
non-perturbative techniques. It contains a brief introduction of quark-gluon
plasma (QGP) and discussion on various signatures along with a motivation for
this thesis work. It presents the basic mathematical tools and ingredients
required for the thesis, i.e. basics of QCD, Imaginary and Real Time Formalism,
Hard Thermal Loop perturbation theory (HTLpt), Gribov-Zwanziger (GZ) action,
the Correlation Function along with the Spectral Function and Operator Product
Expansion (OPE) and QCD in magnetized medium. OPE is used to compute the
dilepton rate in intermediate mass range by incorporating the non-perturbative
dynamics of QCD through the inclusion of non-vanishing quark and gluon
condensates in combination with the Green functions in momentum space. Also the
magnetic scale (g^2T) in the HTL perturbation theory, related to the confining
properties of the QCD is taken into account using the GZ action through a mass
parameter, which reflects a new space-like quark mode in the collective
excitation. The impact of this new exciting mode on the DPR has been studied
and its important consequences has been discussed. A hot magnetized medium
introduces another scale in the system in addition to temperature.
Electromagnetic spectral properties and DPR are studied completely analytically
in presence of both strong and weak background magnetic fields at finite
temperature. The Debye screening in a hot and magnetized medium has been
studied which reveals some of the intriguing properties of the medium in
presence of both strong and weak magnetic field. Also an important quantity
that characterizes the QGP, namely quark number susceptibility has been
investigated. Most of the non-perturbative results discussed in this thesis are
compared with those of perturbative ones and lattice QCD.
