Relativistic Configuration States and Quantum Fields

A. J. K�lnay

W-Y. P. Hwang, Ta‐You Wu

Vladislav G. Bagrov, I. L. Buchbinder, Dmitri M Gitman

The problem of the construction of coherent states of relativistic particles (bosons and fermions) in electromagnetic fields has been solved. The states discovered are exact solutions to the Klein-Gordon and Dirac equations; the wavefunctions of the particles are found in the homogeneous magnetic and electric fields and the Redmond configuration field, as well as in the plane-wave field. The formulation of relativistic quantum mechanics is used on the 'null' plane.

Bruno Galvan

In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is to modify the Lebesgue measure of configuration space of many particles by adding singular measures over the subspaces of configuration space in which the positions of two or more particles coincide.

Art Hobson

Kevin Hernández, Elías Castellanos

We investigate localized, self-bound scalar-field configurations in relativistic Bose–Einstein condensates described by a nonlinear Klein–Gordon equation with cubic and logarithmic interactions. Working in the condensate rest frame, we formulate the corresponding relativistic field theory, derive the conserved Noether current and energy–momentum tensor, and obtain the relativistic chemical potential governing self-confinement, which reduces to a generalized logarithmic Gross–Pitaevskii equation in the nonrelativistic limit. Using a Gaussian variational approach, the field dynamics are reduced to a single collective coordinate describing the condensate width. We derive an exact cubic equation for the equilibrium radius and establish a quantitative stability criterion demonstrating that the logarithmic interaction, rather than the relativistic mass term, provides the restoring mechanism responsible for confinement. Numerical simulations for 7 Li, [Formula: see text]Rb and [Formula: see text]Na confirm dynamically stable, localized configurations exhibiting bounded breathing oscillations within the predicted stability regime, with an equilibrium radius that scales linearly with particle number. These self-confined states display the characteristic dynamical signatures of droplet-like configurations, suggesting that logarithmic nonlinearities provide an alternative mechanism for the formation of localized condensates beyond the conventional Lee–Huang–Yang stabilization scenario.