الخلاصة:
In this work, we are interested to the process of pair creation of spin
0 and 1/2 particle from the vacuum, by using the Schwinger
technique based on the determination of the effective action and also
on the obtaining of solution of Klein Gordon and Dirac equations
when the potential has a dependency in vt, v being the velocity v
(constant).
In the process of pair creation, first a field of wave type Volkov and
non-abelian with N generators (SU (N)) is considered in order to
calculate analytically and algebraically the probability by using
simple transformations. We have established for this form of
interaction, that it is impossible to create particle pairs for the two
cases of spin 0 and 1/2.
In the framework of the geometry of the non-commutative spacetime, the same creation process is reconsidered with as interactions,
the plane wave and the constant and uniform electromagnetic field.
As a result, it was shown that the plane wave has no influence on the
creative process and that the probability with a constant electric field
is modified and that the magnetic field, only, can not create particle
pairs.
Finally, thanks to the invariance of Lorentz transformation the Klein
Gordon and Dirac equations with a potential moving with a constant
velocity v, it has been shown that solutions are obtained from these
same equations with a static potential (not mobile) i.e. independent
of time. As a special case, the form of potential "step" was considered
mobile.
