elte

Péter Pósfay

PhD student, Eötvös University, Budapest

pospet at caesar.elte.hu
posfay.peter at wigner.mta.hu
wigner
Research interests
ERGE Quantum field theory and Functional Renormalization Group (FRG).
FRG is a general method for calculating the effective action of a system in a non-perturbative way. It can incorporate the effect of quantum fluctuations and yield a full effective action which can be used to calculate thermodynamics.
QGP Compact astrophysical objects and nuclear matter
Neutron stars, magnetars and pulsars are amongst the most dense objects in the present day universe. They serve as a natural laboratory for the study of superdense nuclear matter.
Connection between compact stars, nuclear matter and FRG

In my PhD thesis I use quantum field theory methods to gain better understanding of astrophysical phenomena. My focus is on neutron stars which are possible sources of gravity waves and gamma ray bursts, moreover they are among the most dense objects in the present day universe, hence they can function as a laboratory of nuclear matter under extreme conditions.

My research concentrates on the effect of quantum fluctuations in calculating the equation of state of nuclear matter in neutron stars, which belongs to the low temperature and high density part of the QCD phase diagram. My main goal is to develop effective field theoretical models for the above mentioned part of the QCD phase diagram, which can be used in describing both nuclear matter and neutron stars.

There  are two  main reason I interested in the effect of quantum fluctuations. The first is the challenging nature of the low temperature part of the QCD phase diagram.  At low density  and high temperature the phase diagram is better known, because it is possible to experimentally probe it, and numerical results from lattice QCD are available. Contrary, there are no experimental data or numerical results corresponding to the high density and low temperature part of the phase diagram. It is impossible to produce this state of nuclear matter in experiments, but it can be found in neutron stars. Because of reasons mentioned above one has to resort to effective theories to describe nuclear matter in the low temperature regime. There are three main restrictions to these theories.
They have to reproduce the properties of the nuclear matter in normal conditions which present in nuclei, and they have to be consistent whit the high temperature  measurements and lattice calculations. The third constraint is more indirect. One can calculate the properties of neutron stars which results from using these effective models of nuclear matter. There are two main quantities of neutron stars which can be observed: the mass and the radius of the neutron star. Radius measurements are not as precise as mass measurements because of the small diameter (approx 10 km), and big distance to neutron stars. These measurements always indirect, and model dependent, but they becoming increasingly better nowadays. On the other hand the mass measurements are very accurate, and they provide a very strong restrictions on the equation of state of neutron stars. Since two solar mass neutron stars are observed, it is a very strong constraint on the effective theories of nuclear matter that they should be able to produce stable two solar mass neutron stars. To summarize the effective theories should be in agreement with high temperature calculations and measurements, properties of nuclear matter in nuclei, and they have to be able to produce a two solar mass neutron stars when they applied in those conditions. 
Nowadays there are lot of effective theories which are in very good agreement with the conditions, but they often mean field or one loop calculations.  My interest in the effect of quantum fluctuations is fueled by the fact that it can become a fourth constraint on the effective theories. The reason for this is the masquarade problem: many different effective theories can yield similar equation of state, and neutron star calculations are sensitive only to that. Including quantum fluctuations means little corrections to the equation of state, but they can mean big differences in the phase structure of nuclear matter. Calculating the effect of quantum fluctuations in two effective theories which provide similar equation of state shows their difference in phase structure and better one can be chosen. This is a fourth criterion on effective theories: consistency with quantum field theory.

The second main reason I interested in the effect of quantum fluctuations is an astrophysical one. Neutron star binaries are very important sources of gravity waves. Analyzing the emitted gravity waves one can get more information on the equation of state of nuclear matter. Since in the collision of neutron stars binaries they are not in equilibrium phase transitions of nuclear matter and hence the phase structure of nuclear matter are more important. As I wrote above the effect of quantum fluctuations is important in this question.

 To calculate the effect of quantum fluctuations I employ the functional renormalization group (FRG) method. FRG is a general, non-perturbative procedure to calculate the effective action of a system. It provides a smooth transition from the microscopic theory to the macroscopic quantities. Performing these calculations at finite chemical potential, and temperature one can arrive at the equation of state of nuclear matter which includes quantum fluctuations.