The theoretical predictions under this framework, for example the cross sections of particle collisions in an accelerator, are extremely good to describe experimental data.
This is a framework to describe a wide class of phenomena in particle physics in the energy range covered by all experiments, i.e., a tool to deal with complicated many body problems or interacting system. The conventional quantum field theory is formalized at zero temperature. The dilepton production rates from quark–gluon plasma with these non-perturbative effects have been computed and discussed in details. The general features of the deconfined QCD medium have also been outlined with non-perturbative effects like gluon condensate and Gribov–Zwanziger action. The leading order (LO), next-to-leading order (NLO) and next-to-next-leading order (NNLO) free energy and pressure for deconfined QCD medium created in heavy-ion collisions have been computed within HTLpt. As an effective field theory approach the HTL resummation and the HTL perturbation theory (HTLpt) have been introduced.
Then, some subtleties of finite temperature field theory have been outlined. Therefore, one learns about the collective excitations in a QCD plasma from the acquired knowledge of QED plasma excitations. In HTL approximation, the generalisation of QED results of two point functions to quantum chromodynamics (QCD) have been outlined that mostly involve group theoretical factors. The spectral representation of fermion and gauge boson propagators have been obtained. The dispersion properties and collective excitations of both electron and photon in a material medium in presence of a heat bath have been presented. The one-loop self-energy for electron and photon in QED have been obtained in hard thermal loop (HTL) approximation. The quantum electrodynamics (QED) and gauge fixing have been discussed in details. Then the free partition functions and thermodynamic quantities for scalar, fermion and gauge field, and interacting scalar field have been obtained from first principle calculation.
The imaginary time has also been introduced from the relation between the functional integral and the partition function. The basic features of general two point functions, such as self-energy and propagator, for both fermions and bosons in presence of a heat bath have been discussed. The tadpole diagram in \(\lambda \phi ^4\) theory and the self-energy in \(\lambda \phi ^3\) theory have been computed and their consequences have also been discussed. Green’s function both in Minkowski time as well as in Euclidean time has been derived. The prescription to perform frequency sum for boson and fermion has been discussed in detail. The imaginary time formalism has been introduced through both the operatorial and the functional integration method. In this article an introduction to the thermal field theory within imaginary time vis-a-vis Matsubara formalism has been discussed in detail.
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