Speaker
Description
I will present the full second-order effective Hamiltonian of QCD, computed and renormalized using the renormalization group procedure for effective particles (RGPEP) and the canonical Hamiltonian as the starting point. The infrared singularities are regulated by a small gluon mass, and the final Hamiltonian is obtained in the limit of that mass approaching zero. We show that the matrix elements of the effective Hamiltonian between color singlet states are well defined in that limit, while nonsinglet states lead to logarithmically diverging matrix elements. This statement can be made for the entire Fock space because an interplay between mass terms and one gluon exchange terms in the Hamiltonian generates a Casimir operator multiplied by the logarithm of the regulating gluon mass. Therefore, the computed Hamiltonian forms a sound basis for numerical computations using either classical or quantum computers.
Additionally, I propose a new way of interpreting the zero-mode problem as a problem of finding self-adjoint extensions of the effective Hamiltonian, which is only defined as a symmetric operator or a symmetric form.