perturbation theory and time axis

[AntonioLao]

The successful application of Feynman diagram for all calculations in QED testified the power and effectiveness of perturbation theory and its method of approximation. However, many physicists would rather calculate without it. The problem is they do not know how.

In view of the conceptual existence of time axis, there is now good reason for believing that perturbation theory has become unavoidable in mathematical analysis as an induction of approximation into an otherwise exact science. This indicates that WKB approximation, power series expansion, asymptotic expansion, Taylor series expansion or any other approximations all become valid justification for their application in a search for a final physical theory.

The equivalent definition of a time axis is the proper time [math]d\tau[/math] of a Minkowsky four dimensional coordinate system such that the [math]\tau[/math] derivative of an infinitesimal interval of time [math]dt[/math] is equal to the [math]\gamma [/math] factor of special relativity.

[math]\gamma=\frac{dt}{d\tau}=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}=[/math]

Furthermore, the application of the ta operator, [math]\frac{\partial x_i}{\partial}[/math], to the inverse of [math]\tau[/math] or its Legendre transform gives the constant of light speed whose square gives a Lorentz invariance for the inner product of fundamental acceleration and fundamental length, [math]\mathbf{a} \cdot \mathbf{r} = c^2[/math].

[Guille]

Do you think there is a way of avoiding perturbation theory in mathematical analyse?

[AntonioLao]

GUILLE,

At this point, I don't know how to use perturbation theory to do any approximate computation. All my computations are based on matrix multiplications with integers solutions.

[Guille]

GUILLE,

At this point, I don't know how to use perturbation theory to do any approximate computation. All my computations are based on matrix multiplications with integers solutions.

Can there be made computations based on tensors/tensor analysis?

[AntonioLao]

GUILLE,

I don't know how to do tensor computations either, although tensors are written in matrices. That's as far as I know.