From the analysis of the harmonic oscillator, Planck proved the existence of a lowest nonzero energy level of the vacuum state, the Zero Point Energy (ZPE). This state generally includes photon-like electromagnetic oscillations, both with and without associated electric charges. It manifests itself in the Casimir force arising in vacuo between two metal plates separated by a small spacing [1] . This force is due to the imposed boundary conditions which lead to the disappearance of a small low-frequency part of the much larger ZPE photon spectrum. It has been shown by experiments to result in a real macroscopic pressure [2] . Consequently, the vacuum is not merely a state of empty space.

The ZPE and the Casimir force imply that there are sources in the vacuum which have to be included into the electromagnetic field equations. This is taken into account in an earlier Lorentz and gauge invariant treatise by the author [3] [4] , including an incorporated four-current which is associated with a nonzero electric field divergence,. It results in broken symmetry of the electric and magnetic field strengths, and. Here the nonzero increases the degrees of freedom, acting somewhat like a hidden variable.

Spatial integration of over the volumes of corresponding elementary particle models results both into nonzero and zero net electric charges, as well as into intrinsic charges of both polarities. The net charges occur in the case of divergent generating functions of the electromagnetic field strengths, thereby leading to point-charge-like solutions, but the intrinsic charges also occur in cases of convergent generating functions [3] . In this connection it should be observed that the quantized field equations become identical with the original equations in which the potentials and current densities are replaced by their expectation values. The resulting revised quantum electrodynamic theory (RQED) [3] [4] thus becomes an alternative to the conventional description of fundamental physics in terms of the Standard Model. Here it should be emphasized that the conventional form of Maxwell’s equations is fully adequate in describing the dynamics of media containing already existing charged particles, such as a plasma. But the same equations can be questioned when considering the fundamental physics of the interior of the elementary particles. One example where Maxwell’s equations fail in the vacuum state of an empty space is given by the photon which has to possess a nonzero spin [3] .

The main purpose of this investigation is to show that the RQED theory can lead to interactions being the same as those due to the conventional strong force. The broken symmetry of RQED results in substantial intrinsic electric charges, even being an order of magnitude larger than the elementary charge, as will be seen in the following parts of this investigation. The mutual interaction force between the intrinsic charges of two particles is therefore expected to become both of short range and two orders of magnitude larger than that which arises from interaction between elementary charges. Such an intrinsic charge interaction thus has basic features being the same as those of the strong nuclear force described by Walker [5] among others. It can debouch into a speculation whether this interaction would interfere with the strong force, or even become an explanation of the latter [4] [6] .

This paper presents a first attempt in studying the intrinsic charge effects and their relation to the strong force, in terms of a simple particle model based on a convergent generating function. It starts in Sections 2 and 3 with the restrictions and basic concepts of the present analysis, continues with the main features of a corresponding particle model in Section 4, and ends with a tentative quark model of the proton and neutron in Section 5.

With the main purpose of demonstrating the effects of the intrinsic charges, a first approach is thus made in terms of a convergent generating function of the electromagnetic field strengths. This avoids the additional complication of a divergent such function, with its related net point-charge behaviour and a related renormalisation process [3] [4] .

There further exists a possibility of studying a compound particle model. This would include a divergent generating function with both net and intrinsic charges, superimposed on a convergent generating function with intrinsic charges only. Also this possibility is postponed to later studies.

The coming analysis will further be restricted to a relatively simple form of generating function, treated as an Ansatz representing a set of various geometrical profiles.

A steady-state particle model will now be elaborated, to form a starting point of the present analysis. For detailed deductions of the underlying theory, reference is made to an earlier treatise [3] . A steady axisymmetric state is considered in a spherical frame, being independent of the angle and having a current density, an electric charge density, an electrostatic potential, a magnetic vector potential, and a velocity vector, where represents the two spin directions. The field equations then take the form

with where stands for a characteristic radial dimension and the operator has the form

With the generating function

having the amplitude and the dimensionless part, self-consistent forms

are obtained for the potentials and the local charge density. This makes the electric and magnetic field strengths and the electric charge density interconnected through the generating function. For a volume element the total integrated charge becomes

where

The total self-force acting on the particle due to the fields, and the charge density becomes [3]

According to Section 0 we restrict the analysis to a convergent and separable generating function given by the Ansatz

with the disposable parameters and, and where is finite for all and. Various values of and represent various but similar profile shapes.

The present theory with its nonzero leads to a nonzero particle rest mass, as given by [3] [7]

With the function

the same mass becomes

where

Treating the present particle model as a boson in a first attempt, the spin is given by [3] [7]

where

Other forms of the spin would only lead to minor changes in the following numerical computations. Combination of relations (13) and (15) results in

The particle configuration being studied here is based on a class of solutions with similar but varying profile shapes. Here a detailed illustration will be presented, as obtained from a special choice of the parameters and. It concerns both the features of the particle model of Section 4 and its combination into a triangular geometry representing a first attempt to make a quark model of the proton and the neutron.

The main purpose of this investigation is to elaborate a model of quarks which form triangular neutron and proton configurations. The model has the following characteristic features:

• There are equal intrinsic electric charges of both polarities.

• These intrinsic charges are an order of magnitude larger than the elementary charge e.

• The electromagnetic field has both electric and magnetic components of which the latter outbalance part but not all of the former.

• The particle model which represents each of the quarks consists of an outer force-free shell defined by the spatial charge distribution, and an inner core within which there are self-forces due to a nonzero electromagnetic field in combination with an intrinsic charge density. The inner core occupies only a few percent of the total particle volume.

• The interaction which arises between two such particles is of short-range character. When gradually shrinking the distance between the particle centra, a corresponding potential distribution is traversed, in the form of one outer barrier, an intermediate well, and an inner barrier.

• The well is of particular interest, because it is associated with a large attractive force. The latter is nearly two orders of magnitude larger than the corresponding repulsive force between two elementary charges.

• The deduced depth of the well is about 7.7 MeV, being nearly of the same magnitude as the binding energy 8 MeV of the neutron.

• The obtained distribution of the barriers and the well makes a stable position of the particle distance possible, near the bottom of the well.

• The present triangular quark model of the neutron and the proton has an outer radius of about and a core radius of about. These values are comparable to the nuclear radius of given for the neutron and the proton [10] .

The results of the present investigation could thus form a first step in a unification of the electromagnetic and the strong nuclear forces.

The author is indebted to MSc Yushan Zhou for a valuable work with the computations of the present analysis. The author also thanks MSc Kerstin Holm- ström for an excellent transcription of the manuscript of the present paper.

Lehnert, B. (2017) Intrinsic Particle Charges and the Strong Force. Journal of Modern Physics, 8, 1053- 1066. https://doi.org/10.4236/jmp.2017.87067