Variational Method in Relativistic Quantum Field Theory

This lecture explores the variational method in relativistic quantum field theory without cutoff, focusing on the philosophy behind attacking real-world quantum field theories non-perturbatively. It covers the Hamiltonian formulation, Feynman's objections, tensor network states, matrix product states, and continuous matrix product states. The instructor discusses the challenges, optimizations, and results of applying the variational method, emphasizing the importance of weakly entangled states and the transition to relativistic continuous matrix product states. The lecture concludes with a comparison to renormalized Hamiltonian truncation and extensions to other theories, highlighting the efficiency and rigor of the proposed approach.