A dimensionally reduced matrix proof of the equivalence between lagrangian and hamiltonian formulations of fermion quantum field theory

Abstract

The transfer matrix has been the standard approach for showing the equivalence between Lagrangian(path integral) and Hamiltonian(operator) formulation of quantum theory. In this thesis we apply an alternative method called dimensionally reduced matrix to prove this equivalence in the context of fermion quantum field theory, and give a comparison of the two approaches. It is found that the features of second quantization and quantization under external field are more manifest in our proof, which are obscured in transfer matrix approach.