Abstract
New exact solution class of Born—Infeld type nonlinear scalar field model is obtained. The variational principle of this model has a specific form which is characteristic for extremal four-dimensional hypersurface or hyper-film in five-dimensional space-time. Obtained solutions are singular solitons propagating with speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions. Such solitons will be called the lightlike ones. The soliton singularity has a form of moving two-dimensional surface or shell. The lightlike soliton can have a set of tubelike singular shells with the appropriate cavities. A twisted lightlike soliton is considered. It is notable that its energy is proportional to its angular momentum in high-frequency approximation. A case with one tubelike cavity is considered. In this case the soliton shell is diffeomorphic to a cylindrical surface with threads by multifilar helix. The shell transverse size of the appropriate finite energy soliton can be converging to zero at infinity. The ideal gas of such lightlike solitons with minimal twist parameter is considered in a finite volume. Explicit conditions provide that the angular momentum of each soliton in the volume equals Planck constant. The equilibrium energy spectral density for the solitons is obtained. It has the form of Planck distribution in some approximation. A beam of the twisted lightlike solitons is considered. The representation of arbitrary polarization for the beam with the twisted lightlike solitons is discussed. It is shown that the effect of mechanical angular momentum transfer to absorbent by the circularly polarized beam can be provided. This effect is well known for photon beam. Thus the soliton solution which have determinate likeness with photon is obtained in particular.
Highlights
A nonlinear space-time scalar field model considered here is known for a long time sufficiently
We obtain its singular exact soliton solutions propagating with the speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions
The presence of field singularities requires an addition of the appropriate singular densities to the action (2.1), (2.3) and in the right side of the equation (2.4). This aspect was considered for the case of nonlinear electrodynamics in the work [4] and it is expanded in the monograph [5]
Summary
A nonlinear space-time scalar field model considered here is known for a long time sufficiently. The model under consideration has a static spherically symmetric solution, which is identical in form to a zero component of the electromagnetic four-vector potential for dyon solution of Born – Infeld electrodynamics [4, 5] This static solution of the scalar model gives the appropriate moving soliton solution with the aid of Lorentz transform. The photon beam could be represented by an appropriate scalar soliton beam In this case an essential space-time nonhomogeneous of soliton solution may provide the necessary symmetry properties for the beam. We obtain its singular exact soliton solutions propagating with the speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions Such solitons will be called the lightlike ones. In this case the beam can have the polarization property and can provide the effect of the mechanical angular momentum transfer to absorbent for the circularly polarization
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