Feynman integral for functional Schr\"{o}dinger equations

TL;DR

This paper develops an infinite-dimensional symbolic calculus to prove the convergence of Feynman integrals for propagators of coherent states in various bosonic quantum models, advancing the mathematical understanding of functional Schrödinger equations.

Contribution

It introduces a new symbolic calculus framework that handles a broad class of Hamiltonians in all Fock representations, ensuring convergence of Feynman integrals for these models.

Findings

Proves convergence of Hamiltonian Feynman integrals for coherent state propagators.

Applies to multiple Fock representations including Cook-Fock, Friedrichs-Fock, and Bargmann-Fock.

Establishes a rigorous mathematical foundation for functional Schrödinger equations in quantum field theory.

Abstract

We consider functional Schr\"{o}dinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional symbolic calculus allows us to prove the convergence of the corresponding Hamiltonian Feynman integrals for propagators of coherent states.