A new type of soliton with particle properties

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Abstract
This paper describes stable field configurations of two scalar fields ϑ (x,y,z,t) and φ (x,y,z,t). The field configurations follow from a simple least action principle based on an energy density which is a function of ϑ, φ, and their first derivatives. The description is Lorentz‐invariant. The structures are of a stringlike type and are characterized by several integers. It is shown, that the simplest closed strings, described by the integers N=1, M=1, P±1, are stable. The structures P=1 and P=−1 are related by mirror symmetry. Three constants enter in the basic action principle: a length l, a constant E with the dimension of energy time length, and a dimensionless parameter γ. All properties of these field configurations have discrete values, which is a direct consequence of the nonlinearity of the basic expression for the energy density. An attempt is made to identify these structures with elementary particles, the electron and the positron in the simplest case P=1 and P=−1. To this aim, the total energy of the field structures is equated to the rest energy of the particles. The constants E, l, and γ are related to the fundamental physical constants h, m, e. The model proposed represents a classical field structure with quantized properties.