Investigations On Entanglement Entropy In Scattering Process

The physics of fermion-fermion scattering plays a crucial role in a wide variety of scattering experiments,which probe the behavior of elementary particles.Nevertheless,these theoretical investigations often focus on classical observables such as cross section and decay rate,since these quantities are simpler to access via experiment.An essential property that distinguishes quantum mechanics from classical mechanics is the possibil-ity of entanglement between different degrees of freedom.Entanglement entropy is a measure of how much a given quantum state is quantum mechanically entangled.In the paper,we investigate issues of entanglement entropy in simple example of fermion-fermion scattering.In Chapter 2,we briefly introduce the relationship of entanglement and decoherence,the definition of entanglement entropy and the basic properties of entanglement entropy.In Chapter 3,we review and investigation the properties and calculation methods of entanglement entropy in momentum space.In momentum space,the degree of freedom of any interacting quantum field theory are entangled,so that the infrared degree of freedom of its vacuum state can be represented by a density matrix with the entanglement entropy which provides entanglement between different degrees of freedom in momentum space.Base on the relation between the density matrix and the conventional Wilsonian effective action,we derive the entanglement entropy and mutual information between subsets of field theoretic degrees at different momentum scales.Subsequently,Kumar used Lorentz invariant normalized ground state to recalculate the entanglement between different modes in the interaction field.It is found that the divergence structure of the entanglement entropy in the momentum space was caused by the existence of spatial higher order derivatives term.In Chpater 4,we study the properties of entanglement entropy in Fermi elastic scat-tering process.Firstly,based on the perturbation method provided by Balasubramanian,the calculations of entanglement entropy between scattering particles in the?~4theory is briefly reviewed.Secondly,when considering the more general scattering case,such as the strong interaction scattering process in the high-energy case,then we introduce a more extensive theoretical method by Peschanski,which uses the fractional wave method to represent the S matrix in the scattering process.Finally,considering the spin de-gree of particles,we research on the behavior of entanglement between different degrees of freedom of scattering fermions.The variation of entanglement entropy between two fermions from an initial state to the final state was computed,with respect to different entanglement between the ingoing particles.This variation of entanglement entropy is found to be proportional to an area quantity,i.e.,the total cross section.In Chapter 5,we investigation the properties of entanglement entropy among scat-tering particles as observed from different inertial moving frames,based on an exemplary QED process e~+e~-??~+?~-.By the explicit calculations of the Wigner rotation,the entanglement entropy of ingoing and outgoing particles are found to be Lorentz invari-ant.We also study the behavior of the entanglement between spin degrees of freedom among scattering particles in moving frames.In the large boost,the spin entanglement entropy of outgoing particles reaches a constant value that only depends on degree of entanglement for ingoing particles.In the last chapter,we give out the conclusions and some outlook in this dissertation.