Canonical approach to unification?..

[eljose79]

I have watched that in physics or string theory perturbation is used..but could we obtain a unifying theory of physics using canonical theory?..i mean take the Lagrangian take the hamiltonian and quantizy the moment Pab by introducing functional derivatives..

[instanton]

Yes we can certainly do that.
But, you have to realise that even in one two dimensional spacetime (one space one time) your functional "Schrodinger equation" is a infinite number of coupled partial differential equation, which makes it very difficult to solve.

There are certainly some advantage of using canonical method over covariant perturbation theory especially if you want to prob some non-perturbative regime like question regarding vacua or solitonic objects.

Instanton