Relationship Between Quantum Field Theory And Non-Hermitian Hamiltonian

Quantum field theory is the highest accuracy theory to interpret some type of particle experiment, however, it is still not perfect with many basic problems unexplained. The Hamiltonian is the most important physical quantity in quantum mechanics, and it is the most important component of Schrodinger equation. The physical meaning of the non-Hermitian Hamiltonian is not very clear so that correlation studies has undergone many ups and downs at least half a century. Recently non-Hermitian Hamiltonians is in some way related to PT symmetry, which causes interest on the part of the researchers.The Section five of Chapter three and all Chapter four are the main work of this thesis. This thesis focuses on gauge transformation and Schrodinger equation in quantum field theory, looking for a closer relationship between quantum mechanics and quantum field theory, in order to mutual inspiration of non-Hermitian Hamiltonians with quantum field theory. For this purpose, this paper deduce Jacques- Hamilton equation anew on the basis of the lattice hypothesis of quantum field theory. So we are able to make a brief discussion on the boundary condition of the application of the Schrodinger equation. Then contacting gauge transformation invariance, we are more clear that the Schrodinger equation is one connection of field and particle in quantum field theory. From the boundary conditions, the Schrodinger equation reflects the defects of quantum field theory in some degree. So it is clear that the current field structure can only partly explain the non Hermitian Hamiltonian in quantum mechanics. From the understanding of gauge transformation and the expression of Hamiltonian density, Gauge-like transform hides in the gauge transformation. Finally discuss the defects and prospects of quantum field theory.