Canonical Quantization Of Classical Field With Boundary Conditions

The quantization of classical field with boundary conditions was studied. The boundary conditions were teated as constraints in this thesis to quantize the classical field with boundary conditions. The Dirac method and Fadeev-Jackiw method for constrained system were introduced firstly. We analysed canonical quantization of complex scalar field with boundary conditions by Dirac method. I devoted main part to the study of Fadeev-Jackiw method in canonical quantization of classical field with boundary conditions.Making variation for the action of complex scalar field, we get the motion equation and boundary conditions. Defining the Fourier modes as symplectic variables, we can write out Lagrangian function by the symplectic form. And the commutators can be get convienently. The Casimir energy of complex scalar field has been analysed.Making variation for the action of electromagnetic field, we get the motion equation and boundary conditions. Defining the Fourier modes as symplectic variables, we can write out Lagrangian function by the symplectic form. And the commutators can be obtained .Making variation for the action of spin field, we get the motion equation and boundary conditions. Defining the Fourier modes as symplectic variables, we can write out Lagrangian function by the symplectic form. And the commutators can be obtained.The perturbation theory of field with boundary conditions have been studied.We calculated the scattering matress of Moller scattering and Compton scattering and Bahhama scattering.