The Study Of Transverse Momentum Distribution Functions In Basis Light-front Quantization

Basis Light-Front Quantization.(BLFQ)is a non-perturbative,first principles mumerical approach for solving schrodinger equation in quantum field theory.Like Generalized Parton Distribution functions(GPD)and Form Factors of electron,some scientists have calculate those structure functions in BLFQ.In this thesis,we mainly calculated the Transverse Momentum Distribution functions(TMD)and Generalized Transverse Momentum Distribution functions(GTMD)of electron in BLFQ.It is worth to note that we ignore the effect of gauge link and work in the light-cone gauge.By comparing the results of BLFQ with perturbation theory,we find the results of BLFQ have the oscillations around the results of perturbation theory.The reason is that BLFQ uses harmonic oscillator basis in transverse directions.And because the quantum numbers of harmonic oscillators can in principle be arbitrarily large,we introduce transverse basis truncation-Nmax.and find the oscillations become smaller as Nmax increases.We believe better agreement between the results of BLFQ and perturbation theory will be achieved when we use larger Nmax.Meanwhile,according to the calculation,we not only get the information of 3-dimensional momentum of the partons in a dressed electron in TMD,but also calculate the GTMD of electron via introducing transverse momentum transfer.We can also compare those results of GTMD with perturbation theory,and it is reasonable to believe that BLFQ is suitable for calculating the distribution functions.