Sharif Digital Repository

The heavy ion collision experiments are in progress in order to investigate how the Universe has evolved after the Big Bang. The recent observations show that a nearly perfect fluid is produced after heavy ion collisions. An appropriate incorporation of the relativistic hydrodynamics and the field theory would help us to describe the dynamics of QCD (Quantum Chromodynamics) matter under extreme conditions, and to survey the expected phase transitions. The majority of efforts to investigate the characteristics of the QCD plasma are devoted to an ideal, non-dissipative one. To get the results which are highly in accordance with the experiment, it is necessary to bring also in mind the role of... 

Kinetic terms of effective action including derivative of classical field become significant, when we have a dynamical field.These terms have been calculated as a function of the fermionic propagator in NJL model, which is an effective model of QCD. In this thesis, after briefly reviewing
the effect of constant background magnetic field on the propagator considered by Ritus method, we explicitly determine the kinetic terms in terms of Ritus eigenfunctions. Finally, we numerically calculate these terms at finite temperature and chemical potential according to the imaginary time method  

One of the long-lived problems in the theory of quantum chromo dynamics is the violation of parity (P) and charge-parity (CP) symmetries in strong interactions. The existence of gluon configurations sourcing from topology leads to degeneracy in the vacuum structure of the theory. This phenomenon is realized by the addition of an extra term proportional to the parameter to QCD Lagrangian. Experimental estimates of neutron electric dipole, predicts a very small value for this parameter. There is no verified justification for this discrepancy. Recently at the relativistic heavy ion collider laboratory (RHIC) some experimental evidence has been found which indicates local CP violation in... 

Relativistic hydrodynamics and kinetic theory are often used to analyze the experimental data from heavy ion collisions. One of the most important observations is the anisotropy in the number density of the detected particles after the collision in the longitudinal and perpendicular directions with respect to the reaction plane. On the other hand, very strong magnetic fields are created during the early stages of non-central heavy ion collisions. The presence of constant background magnetic fields, aligned in the perpendicular direction to the reaction plane, can be one of reasons for the aforementioned anisotropy in the number density of detected particles. In this thesis, we study the... 

In heavy ion collisions, extremely large electromagnetic fields are produced by fast-moving charged nucleons. They are sufficiently large to affect the low energy QCD processes and thus produce observable effects, whose occurrence is, however, directly related to the lifetime of these fields. In the present dissertation, the evolution of electromagnetic fields is studied in a plasma of quarks and gluons, by analytically solving the equations of relativistic magnetohydrodynamics (RMHD). The onideal Bjorken RMHD is solved by introducing the method of nonconserved charges. Assuming an electromagnetic force-free condition, the electric and magnetic fields are found to be either parallel or... 

In particle physics, spontaneous chiral symmetry breaking generates new phases of quark matter, and leads to significant changes od quark masses. The Nambu-Jona–Lasinio (NJL) model is a useful fermionic model which describes the spontaneous chiral symmetry breaking through the creation of a condensate. This model can be for instance used to determine various phases of Quantum Chromodynamics (QCD) in finite electromagnetic fields. This work consists of several parts. First, we describe the spontaneous chiral symmetry breaking in detail. Second, we extract the NJL model from the Lagrangian density of QCD. Third, we derive a covariant form of the partition function of a fermionic system.... 

Relativistic collisions of heavy ions lead to the formation of a new phase of matter called Quark-Gluon Plasma (QGP). In addition, strong magnetic fields generates in these collisions that its direction is perpendicular to the collision axis. This strong magnetic field affects the dynamics of particles in the QGP, and causes the appearance of the Landau levels in the particle’s energy spectrum. In this master thesis, we investigate the impact of the magnetic field on dilepton production and synchrotron radiation. We calculate the scattering probability of quark and anti-quark annihilation and dilepton creation by taking all Landau Levels into account. Then, by assuming that the magnetic... 

After the review of formation of Landau levels (LL) in non-relativistic quantum mechanics, we have obtained LL in a certain gauge A_μ=(0,-B_0/2 y,B_0/2 x) at 2+1 &3+1 dimension. then give a summary of Quantum Field Theory at non-zero temperature . obtaining LL and two-point Green function in non-uniform magnetic field which determined with A_μ=(0,0,√qB ξe^(-(t+x) ),0).Next we calculate magnetic susceptibility of in such a field with finite chemical potential and temperature. Finally we compare the obtained results with uniform magnetic field one  

In the present thesis, the effect of external magnetic fields on two-flavor Color Superconductive (2SC) phase, as one of the phases in the QCD phase diagram, is studied. To do this, an effective two-flavor Nambu-Jona Lasinio Lagrangian is used, which consists of two mass gaps, s = ?¯qq and ? = ? . The nonzero values of chiral and color mass these gaps induce spontaneous chiral and color symmetry breaking, and consequently two different phases. There is also a third phase, the normal phase, where s = ? = 0. We calculate the transition curves and the critical points in terms of three intensive quantities, the temperature, the chemical potential and the external magnetic field. We study, in... 

The main focus of this dissertation is to investigate the effects of the created background magnetic field on some of the observables that are relevant in heavy ions experiments. Based on the phase diagram of Quantum Chromodynamics, it is expected that in extreme conditions such as high temperature or in dense medium, a new phase of matter arises, which is known as Quark-Gluon Plasma (QGP). Due to the vital role of collective behaviors, this phase behaves similar to a perfect fluid rather than a gas. In addition, the colliding nucleons have potential of creating very strong magnetic fields because of their electric charges and relativistic speeds. Therefore the investigation of the effects... 

Using the general structure of the vacuum polarization tensor П_μν (k_0→0,k) in the infrared (IR) limit, k_0→0 , the ring contribution to the QED effective potential at finite temperature and the nonzero magnetic field is determined beyond the static limit, (k_0→0,k→0). The resulting ring potential is then studied in weak and strong magnetic field limits. In the weak magnetic field limit and at high temperature the improved ring potential consists of a term proportional to T^4 α^(5/2), in addition to the expected term T^4 α^(3/2) arising from the static limit. In the limit of the strong magnetic field, where QED dynamics is dominated by the lowest Landau level, the ring potential includes a... 

In this thesis NJL and quark-meson models, as effective models for quantum chro-modynamics in low energies, are studied mainly. After reviewing models and phe-nomena related to the strong interaction in zero and non-zero temperature, firstly the critical coupling of NJL model for non-zero temperature and chemical potential is calculated. Then, the contribution of ring diagrams in the effective potential of quark-meson model is presented. Finaly, the effect of ring diagrams of quark-meson model on chiral phase transition is investigated. For NJL model, it is shown that the chemical potential lowers the critical coupling for chiral phase transition. Also for quark-meson model, it is shown that... 

One of the most essential concepts for describing neutron stars is investigating their radial mass distribution or mass-radius relation. The aim of this thesis is to evaluate radial mass distribution of neutron stars in the presence of magnetic fields. To achieve this objective we use the Tolman- Oppenheimer-Volkoff equation of hydrostatic equilibrium for non-rotating cases and the Hartle- Thorne equations for rotating cases. olving these equations depends on determination of equation of state of neutron star in the presence of magnetic fields. For determining the corresponding equation of state, one can use QCD-like non-perturbative models, in particular Nambu-Jona- Lasinio (NJL) model. In... 

In the framework of the Standard Model of Particle Physics, Quantum Chromodynamics (QCD) is known to be the only theory which describes the strong nuclear force. Because of the property of asymptotic freedom, perturbative methods fail to describe QCD at low energies. Here, mesons and baryons build the main degrees of freedom of QCD. To describe the dynamics of mesons at low energies, nonperturbative methods are used. The Nambu–Jona-Lasinio (NJL) model is one of the most important effective models, which is used to study the nonperturbative phenomena of QCD at low energies. The Lagrangian density of this model includes a local four-fermion term,which descibes the interaction between the... 

Quantum Chromodynamics (QCD) is the theory of strong interaction. Two main properties of QCD in low energies are chiral symmetry breaking and confinement. At finite temperature, QCD exhibits a certain transition from a chirally broken phase to a chirally restored phase and liberation of color charge. Lattice QCD at finite temperature shows a crossover transition at vanishing or small chemical potential while the model-dependent studies, e.g. the Nambu-Jona--Lasinio model predicts a first-order phase transition at large chemical potentials. The first order and crossover transition lead to the existence of a critical point in the phase diagram of QCD. Determining the nature of the phase... 

We calculate NJL-Model free energy throughthe finite- temperature methods.Then according to the energy-gap equation, we determine symmetric and anti-symmetric phases under Chiral Transformation, in different regions of the phase diagram,with chemical potential() and temperature(T)as control parameter. We conclude with comparing the result of the finite temperature expansion to nonzero chemical potential to the result of,T=0 and finite ,andT=μregime.
 

In this thesis, we review the properties of the two dimensional quantum electrodynamics, called Schwinger model and then we study the noncommutative version of the Schwinger model. The most important properties of the Schwinger model in commutative space are the production of dynamical mass for photon like the Higss mechanism and also the bosonization of the model by integrating out the fermionic degrees of freedom and describing it through the free bosonic action. The first section of this thesis includes two parts. At the first, we investigate the corrections to the dynamical photon mass in the noncommutative Schwinger model by using the photon’s vacuum polarization diagrams at one loop... 

Using the achievements of differential geometry an extended form of descent equations is worked out which leads to a set of modified consistent anomalies. A gauge invariant partition function is also defined for gauge theories with the standard quantization results. It is shown that the (extended) descent equations and consequently the (modified) consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally. Moreover Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations of Translation-invariant quantum field theories are entirely determined by α-cohomology class of star product in all... 

Magnetohydrodynamic is used to study many phenomena. In non-relativistic terms, it can be used to express dynamo theory and to study the evolution of a magnetic field in a conductive fluid medium. In the case of fluid particles having chiral imbalance, the instability associated with this property is observed in the system response to the small perturbation from the equilibrium state. In a relativistic framework, these equations can describe the quark-gluon plasma in the heavy ions collision in a decentralized manner and the nucleus of neutron stars. In many studies, chirality has been considered for such environments. Obtaining the dispersion relation and investigating the response of the...