N-particle Hamiltonians

E. Ruiz

Time evolution of relativistic particle systems can be accomplished by means of a Schrödinger wave equation, provided the Hamiltonian of the N particle system satisfies some commutator equations involving the other generators of a suitable representation of the Poincaré group on the initial data space of the Schrödinger equation. This set of operator equations is solved in the N free particle case. Further, the structure of N interacting particle Hamiltonians is worked out to include second-order relativistic corrections, i.e., (1/c2)-terms. It is shown that Breit and Barker–O’Connell Hamiltonians (nonzero spin particles) and the Bažański Hamiltonian (zero-spin particles) are particular cases of this more general Hamiltonian.

Jose A. Magpantay

There is no relativistic Hamiltonian for many particles systems except for free particles and this has been accepted since the 1960s from the work of Currie, Jordan and Sudarshan, Cannon and Jordan, and Leutwyler. This is the problem we will address in this paper by coupling relativistic particles with a scalar field. The Hamiltonian we derive is explicitly relativistic and in the non-relativistic limit gives a Hamiltonian with two body interaction. However, we find that the Poincare algebra is still not satisfied because of the inherent time delayed interaction in relativistic particle systems.

Jan Dereziński, Christian Gérard

Philip L. Bowers

Mohammad Pouranvari

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode in a one-dimensional free fermion model that undergoes a delocalized–localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigenmode has the same behavior as SPEE of Hamiltonian eigenmode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decrease in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigenmode — which can be obtained through the calculation of moments of SPEE — signature very sharply the phase transition point. These two modes are also compared by calculation of single-particle Rényi entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigenmode can be used as phase detection parameters.