Singular perturbations of a free quantum field Hamiltonian
Mathematical Physics
2019-12-04 v1 math.MP
Abstract
We study solutions of the functional eigenstate equation of a free quantum field Hamiltonian. Admissible solutions are to have a finite norm and a finite eigenvalue w.r.t. the norm and eigenvalue of the ground state of the free theory. We show that in the simple cases of a scalar field and of a vector field in the Coulomb gauge the admissible eigenstates exist and possess negative energy. The functionals can be treated as infinite-dimensional counterparts of the eigenfunctions of the theory of singular perturbations of differential operators, and can be deployed for construction of the renormalized states of models with asymptotic freedom.
Keywords
Cite
@article{arxiv.1912.01458,
title = {Singular perturbations of a free quantum field Hamiltonian},
author = {T. A. Bolokhov},
journal= {arXiv preprint arXiv:1912.01458},
year = {2019}
}
Comments
26 pages