The idea is pretty similar to the idea of extension from 1-dimension to 2-dimensions. A point in 1-dimension is represented in R as x or y. If we take two copies of R, we get the space R ⊗ R in which we can represent a 2-dimensional point i.e. we go from x → (x, y). The operation ⊗ is known as direct product. Let us now examine how we can write a two particle state using two single particle sta...

The problem of Lorentz invariance is treated in the conventional quantum field theory as follows: I) Field variables are transformed as classical quantities. II) Next, the procedure of the second quantization is performed in the new coordinate system. Then the commutation relations are retained to be invariant. However, as Wignerl) has pointed out, the invariance of the commutation relations do...

Using a new fundamental theory based on bit-strings we derive a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/me along the forward and backward light cones executed at velocity fc. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of ra...

The following is an attempt to construct a mathematical model for use in quantum field theory. Although few nonspecialists have had opportunity to become familiar with the language of modern pure mathematics, quantum theory seems to have reached a point where it must use that language if it is to find a genuine escape from the divergence difficulties. Divergence can not be properly coped with w...