With the increasing number of precise observation of neutron stars and their collisions their understanding requires accurate determination of the equation of state of the high density strongly interacting matter. Furthermore, to understand the cooling and the rotational modes of neutron stars, we should calculate the transport properties of its matter at different densities. We would like to use effective field theory using loop expansion and/or functional renormalization group method to determine them. During the PhD the candidate should derive the equation of state of the strongly interacting matter and determine the structure of neutron stars, and determine the viscosities and/or heat capacities its matter.