Quantized Matter Fields In Thick Brane Model

One key feature of extra dimension theories and braneworld scenarios is that the gauge hierarchy problem could be effectively solved in these models.This also makes the characteristic quantum-gravity scale could be compared with the weak scale.To detect quantum gravity and extra dimensional effect in high energy experiments,there are many works emergent to investigate the interaction between various fields in the extra dimension and braneworld models.In previous works,people most focus on the interaction between gravity and particles in the thin brane models,but less attention is paid to the interaction in thick brane models.In this thesis,we mainly study the influence of gravity on the interaction between high energy particles and consider the extra dimensional effect in the high energy physics procedure for thick branes.In chapter 1,we give a brief review on extra dimension theories and braneworld scenarios,including thin and thick brane models,with some works on the interaction between particles of matter fields and gravitons in high energy physics in thin brane models.Next,we introduce some basic concepts and methods in quantum field theory in curved spacetime,as well as the achievements and progress in this field.In Chapter 2,we adopt the method of quantum field theory in curved spacetime to quantize the scalar matter fields in the background of thick brane.We mainly focus on the quantization of massless free scalar fields in the five dimensional spacetime whose metric could give a P¨oschl-Teller potential along the extra dimension.Then we interpret the zero mode of quantum fields as the conventional four dimensional quantum fields and the excited state as the signal from extra dimension.With this statement,it can be seen that the classical potential in the Schr¨odinger-like equation along the extra dimension should have some fine structures to provide a proper mass gap to make the models meet the reality.Based on these results,we give the commutation relations and propagators of the scalar fields.In Chapter 3,with the results from chapter 2,we consider the interactions of fields.We investigate the interaction Lagrange of the form that is linear in the field,which could be regarded as a classical resource that could generate scalar particles.By applying Wick expand to the Hamiltonian,we get the expression of the S matrix.The source is taken to be the form of delta function which is realized by crashing two protons together or by giving a sudden kick to a classical electron.Further,we calculate the particle numbers corresponding to the ground state and first excited state generated by the source.Comparing the particles corresponding to the ground and first excited states,we discuss the effect of extra dimension on the particle reactions.In Chapter 4,we consider a thick brane model where the extra dimensional part of the background spacetime varies with time.In the circumstance,when the time approaches infinity and minus infinity,the background spacetime is asymptotically static.Thus we could define the vacuum state and particle naturally.By calculating the Bogoliubov coefficients corresponding to the transformation between the positive mode functions in these two static stage,we get the particle numbers generated by the effect of an evolutionary extra dimension.In addition,we get the relation between the particle numbers and the value of momentum.We find that the particles generated by the evolution of extra dimension concentrate around a region of low momentum.While the momentum goes to zero or infinity,the number of particle approaches zero.Thus we get a mechanism to produce particles due to the existence of extra dimension.