On the Renormalization of Hamiltonians

Abstract

We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency degrees of freedom and partially diagonalizes the high-energy part, we obtain the effective Hamiltonian for the low energy degrees of freedom. We successfully apply this technique to compute the 2-loop renormalized Hamiltonian in scalar $\lambda {\varphi }^4$ theory.

12 pages, LaTeX

References in corpus (1)

• Flow equations for QED in the light front dynamics

Cited by in corpus (5)

• Coarse Grained Quantum Dynamics
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Exact Renormalization of Wave Functionals yields Continuous MERA
• Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach
• Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom