Quantization of field systems coupled to point-masses

J. Fernando Barbero G., Benito A. Juárez-Aubry, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor

Published 2015-01-21Version 1

We study the Fock quantization of a compound classical system consisting of point masses and a field. We start by studying the details of 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.