Abstract
We consider the model of minimally interacting electromagnetic, gravitational and massive scalar fields free of any additional nonlinearities. In the dimensionless form, the Lagranginan contains only one parameter γ=(mG/e)2 which corresponds to the ratio of gravitational and electromagnetic interactions and, for a typical elementary particle, is about 10−40 in value. However, regular (soliton-like) solutions can exist only for γ≠0, so that gravity would be necessary to form the structure of an (extended) elementary particle. Unfortunately (in the stationary spherically symmetrical case), the numerical procedure breaks in the range γ≤0.9 so that whether the particle-like solutions actually exist in the model remains unclear. Nonetheless, for γ∼1 we obtain, making use of the minimal energy requirement, a discrete set of (horizon-free) electrically charged regular solutions of the Planck’s range mass and dimensions (“maximons”, “planckeons”, etc.). In the limit γ→∞, the model reduces to the well-known coupled system of the Einstein and Klein–Gordon equations. We obtain—to our knowledge—for the first time, the discrete spectrum of neutral soliton-like solutions (“mini-boson stars”, “soliton stars”, etc.)
Highlights
Gravity in Particle PhysicsIt is generally accepted that gravity’s role in the process of the formation and structure of elementary particles is negligible, due to the very small intensity of gravitation interaction
The gyromagnetic ratio is equal to that of Dirac’s fermion [3,4], while “self-quantization” of the electric charge can be naturally achieved in the framework of the so-called algebrodynamic [5]
Even in the case of scalar field, when the field equations allow for spherically symmetric ansatz, the search for regular solutions is an extremely complicated problem
Summary
It is generally accepted that gravity’s role in the process of the formation and structure of elementary particles is negligible, due to the very small intensity of gravitation interaction. In other approaches (see, e.g., [6,7,8]) one claims to construct a realistic model of an extended elementary particle in which gravitational self-interaction plays an essential role These models are based on regular solutions (soliton-like, particle-like, etc.) for a coupled system of the gravitational and other fields’ equations. That is why various solutions can be identified with quite different (astro-)physical objects Such models are semi-classical in origin, since what we seek are regular (soliton-like) solutions to the field equations which possess finite and, sometimes, the discrete spectrum of Noether’s integrals defining the values of corresponding quantum numbers (mass, spin, charge, etc.). The form of effective nonlinearity becomes rigidly fixed by the requirement of gauge invariance
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