Quantization of scalar fields coupled to point-masses

TL;DR

This paper develops a rigorous Fock quantization framework for a system combining point masses and a scalar field, revealing the complex structure of the quantum state space and its non-factorizable nature.

Contribution

It provides a detailed Hamiltonian analysis and explicit construction of the Fock space for a coupled point-mass and scalar field system, highlighting its unique features.

Findings

Constructed the classical solution space precisely.

Established the Fock space for the coupled system.

Showed the Fock space cannot be factorized into separate parts.

Abstract

We study the Fock quantization of a compound classical system consisting of point masses and a scalar field. We consider the Hamiltonian formulation of the model by using the geometric constraint algorithm of Gotay, Nester and Hinds. By relying on this Hamiltonian description, we characterize in a precise way the real Hilbert space of classical solutions to the equations of motion and use it to rigorously construct the Fock space of the system. We finally discuss the structure of this space, in particular the impossibility of writing it in a natural way as a tensor product of Hilbert spaces associated with the point masses and the field, respectively.