Quantization of scalar fields coupled to point masses

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.We would like to thank J Louko for some enlightening discussions. This work has been supported by the Spanish MINECO research grants FIS2012-34379, FIS2014-57387-C3-3-P and the Consolider-Ingenio 2010 Program CPAN (CSD2007–00042). B Juárez-Aubry is supported by CONACYT, México REF 216072/311506 with additional support from Sistema Estatal de Becas, Veracruz, México. Juan Margalef-Bentabol is supported by a ‘la Caixa’ fellowship