Research On Some Quantum Effects Of Dirac Fermions In Curved Space-time

In this thesis,I study several quantum effects of the Dirac fermions in curved space-time.The first part of the thesis is devote to the study of Hawking effects of the Dirac fermions in the black holes as well as the white holes geometry background.In the second part of the thesis using the AdS/CFT duality in the holographic framework,I study the physical properties of the holographic fermionic spectrum under the translation symmetry breaking carefully.This thesis is separated into three chapters:The first chapter briefly presents the research background,significance,current development status at home and abroad as well as the mainly researches content of this paper.In this chapter,I reviews the Damour-Ruffini method and the AdS/CFT duality technology,which is the mainly methods in this thesis.In the second chapter,I discuss Hawking radiation effects of the Dirac fermion in curved space-time.Using the Damour-Ruffini method,I calculate the Hawking radiation of the Dirac fermions from the squashed charged rotating five-dimensional Kaluza-Klein black hole.I find that the obtained Hawking temperature for charged Dirac fermions is the same as for uncharged scalar particles,and the Hawking radiation is related to the size of the extra dimension of the black hole.Our research results again show that the Hawking radiation of black holes is independent of the properties of radiation particles,only related to the intrinsic properties of black holes.Further,we apply the Damour-Ruffini method to study the Hawking radiation of Dirac particles in the black-hole-to-white-hole process.I find that there is a Hawking effect in the white hole from the horizon outside to the horizon inside.This Hawking temperature is a negative value and its absolute value is equal to the Hawking temperature of the black hole.We also find that the Hawking radiation in this process is related to the location of the collapse of the black hole.In the third chapter,according to AdS/CFT duality,I study the physical characteristics of the holographic fermions system in the translation symmetry breaking system.In relativistic fixed point case,for p 0,this holographic fermions system is shown as non-fermi liquid behavior.And with the increase of the Massive Gravity parameter,this phenomenon is more obvious.When p is introduced,I cansee that the formation of Mott gap.In non-relativistic fermionic fixed point case,when p is small value,with increase of Massive Gravity parameter,the peak becomes disperse and the fermi momentum increases.However,for large p,with increase of parameter,the fermi momentum decreases,the bump gradually increase and finally develops into a sharp peak.