where P is the generalized energy-momentum

4-vectorThus in order to satisfy (1) we can express a displacement

4-vector as

Also the potentials "V" and "A" may be considered as a

4-vector potential (56):

In fact, the apparent plurality of possible Clebsch representations of

4-vector potentials creates a unique problem on the types of symmetries hidden in some functional group structures.

The transition was done from the

4-vector of the generalized velocity to a new

4-vector of the Hamiltonian, specifying the energy and the momentum of substance in fundamental fields.

The

4-vector potential, in the background of a cosmic string, reads

The

4-vector [p.sub.a] is the 4-momentum of the electron .

The electrically charged spin-1 [W.sup.[+ or -]] particle is described by a

4-vector function [W.sub.[mu]] x [[W.sub.[mu]] and the electromagnetic 4-potential [A.sub.[mu]] are linear combinations of related quantities [5, see p.

The

4-vector defined by the gradient of the plane monochromatic wave is linked to the energy-momentum

4-vector of a particle by introducing Planck's constant h as

Now, density is a 0-component of a

4-vector and the same is true for energy.

Notice that with the

4-vector formulation Maxwell equation are written in terms of two sets of equations.