(disputed — see talk page)

In electromagnetism, the Lagrangian for an electromagnetic system is

L = L₀ + L_int

where L₀ and L_int are the free and self-interaction lagrangians. The four-vector of density electromagnetic jet, by definition, is

(jets four-vector)

where A is the four-potential of the electromagnetic field. The jets four-vector is the source of the electromagnetic field because Maxwell's equations are

.

It is in all the textbooks of quantum electrodynamics that it is impossible to construct the jets four-vector from the parameters of the electromagnetic field. So usually jets four vector is sum of particles jets eu(s), where e,u are the charge and four velocity of particle. Parameters of electromagnetic field are four potential A(x) and fields bevector

(always here the Clifford algebra formalism is in use).

But in general case any physical field have non zero mass density. Then in general case physical field have parameter u(x) witch is local four velocity vector a field. For example it is well known that for scalar photons (Coulomn field) u² > 0 , for longitudinal photons (magnetic field) u² < 0, for transverse photons u² = 0.

Then taking into account new for field theory parameter u(x) it is possible for electromagnetic field without elementary particles with electric gauge to construct jets four vector. For such creation Bohr's coherence principle is enough, which is a general physical principle.

Jets four vector must be linear function of velocity four vector. So

where c_k are scalar function. Jets four vector must to have such CPTL and phase property as particle jet so c₂ = 0 and scalar function depend from variable F²F ^{+ 2}. Then in first approach

Because for transverses photons jet must be equal zero four vectors A,u are collinear.

Such manner jets four vector in CGS units is

where self interaction constant g change sign at C-transformations. It is similar to particle jet j = eu where electric gauge change and velocity four vector change no sign at C-transformations, Constant g determinate scale for electromagnetic potential, and its is may be known from Lamb shift data. From jets four vector constriction follow . Then gradients freedom of electromagnetic field potential give that jets four vector is not variable by four vector of electromagnetic potential.

In usual three vector form jets four vector is

 :u₀( - E² + H²

and Maxwell's equations transform into Maxwell's nonlinear equations.

These nonlinear equations must be the complete equations for the velocity four vector. It is possible if velocity four vector itself is regarded as potential w-field.